Sachin

Gain complete knowledge on the concept Train Passes a Moving Object in the Same Direction. Learn related formulas like Speed, Time and Distance when a train passes through a moving object in the Same Direction. Get the Step by Step Procedure along with a detailed explanation for the entire concept. Solve Problems on Train Passing a Moving Object in the Same Direction and understand the concept behind them easily.

How to find Time Speed and Distance when a Train Passes a Moving Object in the Same Direction?

Follow the guidelines for calculating the Time Speed and Distance when a Train Passes a Moving Body in the Same Direction. They are as such

Let us consider the length of the train as l mt and the speed of the train is x km/hr

Speed of the Object = y km/hr

Relative Speed = (x-y) km/hr

Time Taken by the train to cross a moving object in the same direction is = Distance/ Relative Speed

= l m/(x-y) km/hr

You can rearrange the equation and find whichever measure you need as a part of your work.

Solved Problems on Train Passes through a Moving Object in the Same Direction

1. A train 150 m long is running at a speed of 50 km/hr. At what time will it pass a man who is running at the speed of 5 km/hr in the same direction in which the train is moving?

Solution:

Length of the Train = 150 m

Speed of the Train = 50 Km/hr

Speed of the Man = 5 km/hr

Relative Speed = Speed of Train – Speed of Man

= 50 – 5

= 45 km/hr

= 45 *5/18

= 12.5 m/sec

Time Taken by Train to Cross the Man = Distance/Speed

= 150 m/12.5 m/sec

= 12 sec

Therefore, Train takes 12 sec to cross the man.

2. Two trains 110 meters and 140 meters long are running in the same direction with speeds of 70 km/hr and 55 km/hr. In how much time will the first train cross the second?

Solution:

Distance Covered = 110+140

= 250 meters

Speed of first train = 70 km/hr

Speed of second train = 55 km/hr

Relative Speed = (70 – 55)

= 15 km/hr

Relative Speed in m/sec = 15*5/18

= 4.1 m/sec

Time taken by first train to cross second = Distance/Speed

= 250 m/4.1 m/sec

= 60.9 sec

Therefore, the first train takes 60.9 sec to cross the second train.

3. A train running at 60 kmph takes 30 seconds to pass a platform. Next, it takes 10 seconds to pass a man walking at 5 kmph in the same direction in which the train is going. Find the length of the train and the length of the platform?

Solution:

Let us consider the length of the train and length of the platform as x and y

Distance traveled by train while crossing the platform is x+y

Time taken to cross the platform is 30 sec

Speed of the train = 60 kmph

= 60 *5/18

= 16.66 m/sec

Time taken by train to cross the platform is

Time = Distance/Speed

30 =(x+y)/16.66  …….(1)

Time taken by train to cross the platform next = 10 sec

Speed of the man = 5 kmph

Relative Speed = 60 kmph – 5 kmph

= 55 kmph

= 55 *5/18

= 15.2 m/sec

Time taken by train to cross the man is

Time = Distance/Speed

10 sec = x/(15.2 m/sec)

x =  152.7 m

By applying the value of x in equation 1 we have

30 =(152.7+y)/16.66

499.8 = 152.7+y

y = 347.1 m

Hence the length of the train and platform are 152.7 m and 347.1 m respectively.

Get full-fledged knowledge when two objects move in opposite direction by going through the complete article. Learn Formula, Solved Examples on Two Bodies Moving in Opposite Direction towards each other. Get Step by Step Solutions for all the Problems on finding Relative Speed, Time and Distance. If two bodies move in opposite direction relative speed is obtained by adding the speeds of both the bodies.

How to Calculate Time Speed and Distance for Two Objects Moving in Opposite Direction?

Consider Two Objects Moving in Opposite Direction with different speeds

Speed of 1st Object = x km/hr

Speed of 2nd Object = y km/hr

Relative Speed = (x+y) km/hr

The speed of One Object with respect to another is called relative speed.

Distance between them = d km

Time after two objects meet = d km/(x+y) km/hr

Distance covered in t hours = relative speed * time

= (x+y) km/hr * t

Solved Examples on Two Object Moving in Opposite Direction

1. Two Athletes are running from the same place at the speed of 10 km/hr and 5 km/hr. find the distance between them after 20 minutes if they move in the opposite direction?

Solution:

Speed of 1st Athlet = 10 km/hr

Speed of 2nd Athlet = 5 km/hr

Relative Speed = (10+5) km/hr

= 15 km/hr

Time = 20 min = 20/60 = 1/3 hr

Distance = Relative Speed * Time

= 15 km/hr * 1/3 hr

= 5 km

Distance between Two Athlets is 5 Km.

2. Two cars travel from the same location at the speed of 10 km/hr and 5 km/hr respectively. Calculate the distance between the cars after 30 minutes given that both cars are traveling in the opposite direction?

Solution:

Speed of 1st Car = 10 km/hr

Speed of 2nd Car = 5 km/hr

Time = 30 minutes = 1/2 hr

Relative Speed of Cars = (10+5) km/hr

= 15 km/hr

Distance between Cars = Relative Speed * Time

= 15 km/hr * 1/2 hr

= 7.5 km

Both cars have a distance of 7.5 km

When Two Objects move in the same direction then their relative speed is calculated by the difference of their speeds. Get to know about the Time and Distance Formulas when two objects move in the same direction. Get to all about the concept objects that move in the same direction by going through the entire article. Learn, how to calculate the Speed when two objects travel in the same direction by checking the solved examples provided.

How to Calculate Speed Time and Distance when Two Objects Move in the Same Direction?

Let us assume two bodies or objects are moving in the same direction having different speeds.

Suppose the Speed of 1st Object is x km/hr

Speed of 2nd Object is y km/hr

Thus, the Relative Speed = (x – y) km/hr[if x>y]

Time taken by two objects to meet = Distance Traveled/Relative Speed

= d km/(x-y) km/hr

We know that Relative Speed is the Speed of the object with respect to one another

Consider the taken after both the bodies meet = t hrs

Distance covered in t hrs = Time * Relative Speed

= (x-y)km/hr *t hrs

For better understanding refer to the solved problems explaining how to calculate when two objects move in the same direction.

Solved Problems on Two Objects Moving in the Same Direction

1. Two athletes are running from the same place at the speed of 8 km/hr and 6 km/hr. find the distance between them after 20 minutes if they move in the same direction?

Solution:

Speed of Athlet A = 8 km/hr

Speed of Athlet B = 6 km/hr

Time = 20 mins = 1/3 hr

Relative Speed = (8-6) km/hr = 2 km/hr

Distance traveled by them = Relative Speed of Athlets/Time Taken

= 2 km/hr/(1/3) hr

= 6 km

Distance between after they travel for 20 mins is 6 Km.

2. Two vehicles are traveling from the same location at the speed of 10 km/hr and 7 km/hr respectively. Calculate the distance between the vehicles after 15 minutes given that both vehicles are traveling in the same direction?

Solution:

Speed of first Vehicle = 10 km/hr

Speed of second Vehicle = 7 km/hr

Relative Speed = (10-7) km/hr

= 3 km/hr

Time = 15 minutes = 15/60 = 1/4 hr

Distance between both the vehicles = Relative Speed * Time

= 3km/hr *1/4 hr

= 3/4 km

= 0.75 km

Therefore, the distance between both the vehicles is 0.75 km

Work with the Problems on Calculating Time and learn how to find Time when Speed and Distance are given. Know the Relationship between Speed Time and Distance with the formula provided. Check Worked out Examples for Distance with Solutions and cross-check your solutions while practicing. Check different types of Time Questions followed by illustrations for a better understanding of the concepts. Practice each of the Time Word Problems provided and score better grades in the exam.

Solved Time Questions with Answers

1. A car travel 70 km in 30 minutes. In how much time will it cover 120 km?

Solution:

Speed = Distance/Time

= 70 km/1/2 hr

= 140 kmph

Speed = Distance/Time

140 kmph = 120 km/Time

Time = 120 km/140 kmph

= 0.85 hr

car takes 0.85 hr to cover the distance 120 km.

2. Vinay covers 180 km by car at a speed of 60 km/hr. find the time taken to cover this distance?

Solution:

Speed = 60 km/hr

Distance = 180 km

Speed = Distance/Time

60 km/hr = 180 km/Time

Time = 180 km/60 km/hr

= 3 hr

Vinay takes 3 hrs to cover the distance 180 km at a speed of 60 km/hr.

3. A train covers a distance of 45 km in 20 minutes. Find the time taken by it to cover the same distance if its speed is decreased by 12 km/hr?

Solution:

Distance covered by train = 45 km

Time taken = 20 min = 20/60 = 1/3 hr

Speed of the train = Distance covered/Time taken

= 45km/1/3 hr

= 135 km/hr

Reduced Speed = 135 km/hr – 12 km/hr

= 123 km/hr

Time = Distance Traveled/Speed

= 45/123

= 0.365hr

= 0.365*60 min

= 21.95 min

4. A man is walking at a speed of 5 km per hour. After every km, he takes a rest for 3 minutes. How much time will it take to cover a distance of 6 km?

Solution:

Rest time = Number of rests * time of each rest

= 5*3 minutes

= 15 minutes

Total Time Taken = Distance/Speed +Rest Time

= (6/5)*60+15 minutes

= 72+15

= 87 minutes

5. A car takes 3 hours to cover a distance if it travels at a speed of 45 mph. What should be its speed to cover the same distance in 2 hours?

Solution:

Distance = Speed *Time

= 45mph*3 hr= 135 miles

Speed = Distance/Time

= 135 miles/2 hrs

= 67.5 miles per hour

Therefore, car needs to travel at a speed of 67.5 miles per hour in order to travel a distance of 135 miles in a time of 2 hrs.

Find the Distance Problems in which an object will travel for a certain distance in a given period of time. Learn the Formula to Calculated Distance When Time and Speed are given. Refer to Solved Problems on Calculating Distance and understand the logic behind them. You can see out Time and Distance concept to know everything in detail. Practice the questions on finding distance and get the answers too from our page. Detailed Solutions makes it easy for you to grasp the concept.

Formula to Calculate the Distance = Speed * Time

Distance Word Problems Examples

1. A train moves at a speed of 45 km/hr. How far will it travel in 30 minutes?

Solution:

Speed of the Train = 45 kmph

Time = 30 min = 1/2 hr

Distance = Speed * Time

= 45Kmph*1/2 hr

= 22.5 Km

Therefore, the train travels a distance of 22.5 km

2. If a motorist moves with a speed of 40 km/hr and covers the distance from place A to B in 2 hours, find the distance between places A and B?

Solution:

Speed = 40 km/hr

Time taken to travel from Place A to Place B = 2 hrs

Distance = Speed*Time

= 40kmph*2 hr

= 80 km

Therefore, the distance between places A and B is 80 km.

3. How much father can an interstate bus go traveling 80 km/hr rather than 50 km/hr in 3 hours?

Solution:

Distance = Speed *Time

If Speed = 80 km/hr

Time = 3 hrs

Distance = 80*3

= 240 km

If Speed = 50 km/hr

Time = 3 hrs

Distance = Speed * Time

= 50*3

= 150 km

Difference between Distances = 240 km – 150 km

= 90 km

4. Sound travels at a speed of 1100 km in one hour. How many meters will it travel in one second?

Solution:

Speed = 1100 kmph

To convert kmph to m/sec multiply with 5/18

= 1100*5/18

= 305.55 m/sec

5. A car travels at a speed of 72 km/hr. How many meters will it travel in 1 second?

Solution:

Speed = 72 km/hr

To convert kmph to m/sec multiply with 5/18

= 72*5/18

= 20 m/sec

6. Mohan drives a car at a uniform speed of 40 km/hr, find how much distance is covered in 120 minutes?

Solution:

Speed = 40 km/hr

Time = 120 minutes = 2 hrs

Distance = Speed*Time

= 40 km/hr*2 hr

= 80 km

7. A car takes 2 hours to cover a distance if it travels at a speed of 30 kmph. What should be its speed to cover the same distance in 1 hour?

Solution:

Speed = 30 kmph

Time = 2hrs

Distance = Speed*TIme

= 30 kmph*2 hr

= 60 Km

Speed = ?

Distance = 60 km

Time = 1 hr

Speed = Distance/Time

= 60 km/1 hr

= 60 kmph

Solve different types of problems on calculating speed and get acquainted with various models of questions asked in your exams. Be aware of the Formula to Calculate and Relationship between Speed Time and Distance. Practice Speed Problems on a regular basis so that you can be confident while attempting the exams. We even provided solutions for all the Questions provided and explained everything in detail for better understanding. Try to solve the Speed Questions on your own and then cross-check where you are lagging.

We know the Speed of the Object is nothing but the distance traveled by the object in unit time.

Formula to find out Speed is given by Speed = Distance/Time

Word Problems on Calculating Speed

1.  A man walks 25 km in 6 hours. Find the speed of the man?

Solution:
Distance traveled = 25 km
Time taken to travel = 6 hours
Speed of Man = Distance traveled/Time taken
= 25km/6hr
= 4.16 km/hr
Therefore, a man travels at a speed of 4.16 km/hr

2. A car covers a distance of 420 m in 1 minute whereas a train covers 70 km in 30 minutes. Find the ratio of their speeds?

Solution:
Speed of the Car = Distance Traveled/Time Taken
= 420m/60 sec
= 7 m/sec

Speed of the Train = Distance Traveled/Time Taken
= 70 km/1/2 hr
= 140 km/hr

To convert it into m/sec multiply with 5/18
= 140*5/18
= 38.8 m/sec
= 39 m/sec (Approx)
Ratio of Speeds = 7:39

3. A car moves from A to B at a speed of 70 km/hr and comes back from B to A at a speed of 40 km/hr. Find its average speed during the journey?

Solution:
Since the distance traveled is the same the Average Speed= (x+y)/2 where x, y are two different speeds
Substitute the Speeds in the given formula
Average Speed = (70+40)/2
= 110/2
= 55 km/hr
The Average Speed of the Car is 55 km/hr

4. A bus covers a certain distance in 45 minutes if it runs at a speed of 50 km/hr. What must be the speed of the bus in order to reduce the time of journey by 20 minutes?

Solution:
Speed = Distance/Time
50 = x/3/4
50 = 4x/3
4x = 150
x = 150/4
= 37.5 km

Now by applying the same formula we can find the speed

Now, time = 40 mins or 0.66 hr since the journey is reduced by 20 mins

S = Distance/Time
= 37.5/0.66
= 56.81 km/hr

5. Ram traveled 200 km in 3 hours by train and then traveled 140 km in 3 hours by car and 5 km in 1/2 hour by cycle. What is the average speed during the whole journey?

Solution:
Distance traveled by Train is 200 km in 3 hours
Distance Traveled by Car is 140 km in 3 hours
Distance Traveled by Cycle is 5 km in 1/2 hour
Average Speed = Total Distance/Total Time
= (200+140+5)/(3+3+1/2)
= 345/6 1/2
= 345/(13/2)”
= 345*2/13
= 53.07 km/hr

6. A train covers 150 km in 3 hours. Find its speed?

Solution:
Speed = Distance/Time
= 150 km/3 hr
= 50 km/hr
Therefore, Speed of the Train is 50 km/hr.

Learn completely on how to convert from one unit of speed to others from here. Practice the Questions in Conversion of Units of Speed here and get a good hold of the concept. Convert from km/hr to m/sec and m/sec to km/hr easily by going through the further sections. To know more about Speed Time and Distance you can always look up to us. Check out Solved Examples on Speed Conversions so that you can solve related problems on your own. Step by Step solutions provided makes it easy for you to understand the Units of Speed Conversion in an effective manner.

How to Convert Km/hr to m/sec?

To convert Km/hr to m/sec follow the below listed guidelines. They are as such

We know 1 km = 1000m and 1 hour = 60 minutes and in turn 1 minute = 60 sec

1 hour = 60*60 = 3600 sec

Dividing km/hr we have = 1000m/3600sec

On simplifying we have km/hr = 5/18 m/sec

Therefore to convert from km/hr we simply multiply with 5/18.

Solved Problems on Converting Km/hr to m/sec

1. Convert 54 km/hr to m/sec?

Solution:

To convert, 54 km/hr to m/sec simply multiply with 5/18

= 54*5/18

= 15 m/sec

Therefore 54km/hr converted to m/sec is 15m/sec.

2. The speed of the bike is 108 km/hr, what is its speed in m/sec?

Solution:

Given Speed of Bike = 108 km/hr

To obtain the Speed in m/sec simply multiply with 5/18

= 108*5/18

= 30 m/sec

Therefore, the Speed of the Bike is 30 m/sec.

3. A car covers a distance of 120 km in the first three hours, 50 km in the next 1 hour, and 25 km in the next 1/2 hour. Convert the speed into m/sec?

Solution:

Total Distance traveled by the Car = (120+50+25) = 195 km

Total Time Taken = (3+1+1/2) = 4 1/2 hrs

Speed of the Car = 195km/4.5 hr = 43.3 km/hr

Speed of the Car in m/sec = 43.3*18/5

= 155.88 m/sec

How to Convert m/sec to km/hr?

Follow the below listed guidelines inorder to change between m/sec to km/hr

We know 1km = 1000m

thus, 1m = 1/1000 km

1 hour = 3600 sec

thus, 1 sec = 1/3600 hr

applying the same we have 1 m/1 sec = (1/1000km)/(1/3600 hr)

= 3600km/1000hr

= 18/5 km/hr

Therefore, to convert from m/sec to km/hr simply multiply with 18/5

Solved Problems on Converting m/sec to km/hr

1. Convert 60 m/sec to km/hr?

Solution:

Given 60 m/sec

to change to km/hr multiply with 18/5

= 60*18/5

= 216 km/hr

2. The speed of a cyclist is 15 m/sec. find the speed in km/hr?

Solution:

Speed of a Cyclist = 15 m/sec

To convert to km/hr multiply with 18/5

= 15*18/5

= 54 km/hr

Get the solutions for the Practice test on Area and Perimeter of Square here. Students can improve their math skills by solving the practice test on the area and perimeter of the square in 2D Mensuration. Scroll down this page to find the various methods to solve the problems on the Area and Perimeter of the square. Go through the questions and try to solve the problems using the area and perimeter of the square formulas.

Formula for Area and Perimeter of Square

• Area of square = s × s = s²
• The perimeter of the square = 4s
• Diagonal of the square = √2 × a

Word Problems on Area and Perimeter of Square

1. Find the area of the square whose side is 6cm.

Solution:

Given,
side = 6cm
Area of square = s × s = s²
A = 6cm × 6cm
A = 36 sq.cm
Thus the area of the square is 36 sq.centimeters.

2. The side of the square is 48m. Find the area and perimeter.

Solution:

Given that,
side of the square = 48m
To find the area of the square
We know that,
Area of square = s × s = s²
A = 48m × 48m
A = 2304 sq.m
Thus the Area of the square is 2304 sq.m.
Now find the perimeter of the square
P = 4a
P = 4(48)
P = 192 cm
Therefore the perimeter of the square is 192 cm.

3. One side of the square is 7m. Find
i. Area
ii. Perimeter
iii. Diagonal

Solution:

Given,
Side of the square = 7m
i. Area:
We know that,
Area of square = s × s = s²
A = 7m × 7m
A = 49 sq. meter
Thus the area of the square is 49 sq. m.
ii. Perimeter:
We know that,
The perimeter of the square = 4a
P = 4 × 7m
P = 28m
Thus the perimeter of the square is 28 meters.
iii. Diagonal:
We know that,
Diagonal of the square = √2 × a
D = √2 × 7m
D = 9.89 meters
Thus the diagonal of the square is 9.89 meters.

4. The side of the square is 60cm. Find the perimeter of the square.

Solution:

Given,
The side of the square is 60cm.
P = 4a
P = 4 × 60cm
P = 240cm.
Therefore the perimeter of the square is 240 centimeters.

5. The Perimeter of the square is 96cm. Find the side of the square.

Solution:

Given that,
The perimeter of the square is 96cm.
P = 4a
96cm = 4a
a = 96/4
a = 24cm
Thus the side of the square is 24cm.

6. The cost of cementing a square yard at ₹ 2 per Square Metre is ₹800. Find the cost of fencing it at a rate of ₹5 per meter.

Solution:

Given,
The cost of cementing a square yard at ₹ 2 per Square Metre is ₹800.
Let the side be x meters.
Rate of cementing = ₹ 2 per m²
Total cost = 800
Area for cementing = 800/2 = 400
x² = 400
x = 20
Perimeter of the yard = 4a
P = 4 × 20m = 80m
Rate of fencing = ₹5 per meter
Total cost of fencing the square yard is 80 × 5
= ₹400
Therefore the cost of fencing it at a rate of ₹5 per meter is ₹400.

7. What is the diagonal and perimeter of the square if the side is 4cm.

Solution:

Given,
The side of the square is 4cm.
Perimeter of the square = 4a
P = 4(4cm)
P = 16cm
We know that,
Diagonal of the square = √2 × a
D = √2 × a
D = √2 × 4
D = 5.65 cm.
Thus the diagonal of the square is 5.65cm.

8. The area of the square field is 144ft². Find the side, perimeter, and diagonal of the square field.

Solution:

Given that,
The area of the square field is 144ft²
Area of square = s × s = s²
144 = s²
s² = 144
s = √144 = 12ft
Thus the side of the square field is 12 ft.
The perimeter of the square = 4a
P = 4 × 12ft = 48ft
Thus the perimeter of the square field is 48 feet.
Diagonal of the square = √2 × a
D = √2 × a
D = √2 × 12
D = 16.9 feet
Therefore the diagonal of the square is 16.9 feet.

9. The diagonal of the square is 4√2cm. Find the area and perimeter of the square?

Solution: Given,
The diagonal of the square is 4√2cm.
Area of square = s × s = s²
A = 4 × 4 = 16 sq.cm
The perimeter of the square = 4a
P = 4 × 4 = 16cm
Thus the area and perimeter of the square is 16 sq. cm and 16 cm.

10. Find the perimeter of the square whose sides are
i. 2 cm
ii. 7cm
iii. 16cm

Solution:

Given,
i. a = 2 cm
We know that,
The perimeter of the square = 4a
P = 4(2cm)
P = 8cm
Thus the perimeter of the square is 8cm.
ii. a = 7cm
We know that,
The perimeter of the square = 4a
P = 4(7cm)
P = 28 cm
Thus the perimeter of the square is 28cm.
iii. a = 16cm
We know that,
The perimeter of the square = 4a
P = 4(16cm)
P = 64cm
Thus the perimeter of the square is 64 cm.

Practice test on Area and Perimeter of Rectangle helps to enhance the math skills. Test your knowledge on mensuration by practice the problems on the Area and Perimeter of the Rectangle. Use the Area and Perimeter of the Rectangle Formula to solve the given problems. Look at the below section and start practicing now. The answers for the practice test on the Area and perimeter of the rectangle are given below.

Area and Perimeter of Rectangle Formula

• Area = length × width
• Perimeter = 2(l + w)
• Diagonal = √l² + w²

Area and Perimeter Word Problems with Answers

1. Find the area of the rectangle if the length and breadth are 6m and 5m?

Solution:

Given,
l = 6m
b = 5m
We know that,
Area of the rectangle = l × b
A = 6m × 5m
A = 30 sq. m
Thus the area of the rectangle is 30 square meters.

2. Find the perimeter of the rectangle whose length and width are 15 cm and 10 cm?

Solution:

Given,
l = 15 cm
w = 10 cm
Perimeter of the rectangle = l + l + w + w
P = 15cm + 15cm + 10cm + 10cm
P = 30cm + 20cm
P = 50 cm
Thus the perimeter of the rectangle is 50 cm.

3. Find the area and perimeter of the rectangle whose length and breadth are 30cm and 25 cm?

Solution:

Given,
l = 30cm
b = 25cm
We know that,
Area of the rectangle = lb
A = 30cm × 25cm
A = 750 cm²
Perimeter of the rectangle = 2l + 2b
P = 2(30cm) + 2(25cm)
P = 60cm + 50cm
P = 110cm
Therefore the area and perimeter of the rectangle are 750 cm² and 110 cm.

4. Find the diagonal of the rectangle whose length and width are 7cm and 5cm?

Solution:

Given,
L = 7cm
W = 5cm
We know that,
Diagonal = √l² + w²
D = √7² + 5²
D = √49 + 25
D = √74
D = 8.60 cm
Thus the diagonal of the rectangle is 8.60cm.

5. The perimeter of the rectangular field is 169 cm. The length of the rectangular field is 12 cm find the breadth?

Solution:

Given that,
The perimeter of the rectangular field is 169 cm.
The length of the rectangular field is 12 cm
We know that,
Perimeter of the rectangle = 2l + 2b
169cm = 2(12cm) + 2b
169cm = 24cm + 2b
169cm – 24cm = 2b
145cm = 2b
2b = 145cm
b = 145/2 = 72.5 cm
Therefore the breadth of the rectangular field is 72.5 cm.

6. The length and breadth of a rectangular field are equal to 300 m and 200 m respectively. Find the cost of the grass to be planted in it at the rate of ₹ 2 per square meter?

Solution:

Given that,
The length and breadth of a rectangular field are equal to 300 m and 200 m.
We know that,
Area of the rectangle = lb
A = 300m × 200m
A = 60,000m²
Cost of the grass to be planted in it at the rate of ₹ 2 per square meter.
= 2 × 60,000m²
= ₹ 1,20,000
Thus the required cost is ₹ 1,20,000.

7. A rectangular piece of dimension 65mm × 63mm. Find the area of the rectangle?

Solution:

Given,
l = 65mm
w = 63mm
We know that,
Area of the rectangle = lw
A = 65mm × 63mm
A = 4095 sq. mm
Thus the area of the rectangle is 4095 sq. mm.

8. The perimeter of the rectangle is 112 cm. The width is 24cm find the length of the rectangle.

Solution:

Given,
The perimeter of the rectangle is 112 cm.
Width = 24 cm
length =?
We know that,
Perimeter of the rectangle = 2l + 2b
112 cm = 2l + 2(24cm)
112 cm – 48 cm = 2l
64 cm = 2l
l = 64/2
l = 32cm
Therefore the length of the rectangle is 32cm.

9. Given length = 42cm and breadth = 21cm. Find the area of the rectangle.

Solution:

Given,
l = 42cm
b = 21cm
We know that,
Area of the rectangle = lb
A = 42cm × 21cm
A = 882 sq.cm
Thus the area of the rectangle = 882 sq.cm.

10. The length and width of the rectangular plot is 44cm and 40cm. Find the area and perimeter of the rectangular plot.

Solution:

Given,
l = 44cm
w = 40cm
We know that,
Area of the rectangle = lb
A = 44cm × 40cm
A = 1760 sq.cm
Perimeter of the rectangle = 2l + 2b
P = 44cm + 44cm + 40cm + 40cm
P = 88cm + 80cm
P = 168 cm
Therfore the area and perimeter of the rectangular plot is 1760 sq.cm and 168 cm.

The Units of Area Conversion helps to convert the units in Mensuration. Students can know the relationship between the various units with the help of the solved examples. Sometimes it is necessary to convert the units of area conversion to solve the problems in mensuration. Here we will discuss in detail units of area conversion. Know how to convert the area units in this article.

Units of Area Conversion

The relationship between the various units of lengths are as follows,

• 1 meter = 100 centimeter
• 1 meter = 10 decimeter
• 1 hm = 100 meter
• 1 km = 1000 meter
• 1 dam = 10 meters
• 1 km = 10 hm
• 1 dm = 10 cm
• 1 yard = 3 feet
• 1 feet = 0.3048 meters

The units of area conversion are given below

• 1m = 100cm, 1 m² = 10,000 cm²
• 1m = 10 dm, 1 m² = 10 × 10 dm² = 100 dm²
• 1 cm = 10 mm, 1 cm² = 10 × 10 mm² = 100 mm²
• 1 km = 1000 m, 1 km² = 1000 m × 1000 m = 1,000,000m²
• 1 hm = 100 m, 1 hm² = 100m × 100m = 10,000m²
• 1 dam = 10 m, 1 dam² = 10m × 10m = 100 m²
• 1 dm = 10 cm, 1 dm² = 10 cm × 10 cm = 100 cm²
• 1 km = 10 hm, 1 km² = 10 hm × 10 hm = 100 hm²
• 1 hectare = 100 ares
• 1 ft² = 0.09 m²

Solved Examples on Area Conversions

Students are suggested to go through the below example problems to know in deep about the units of area conversion.

1. Convert 2 hectares to square meters?

Solution:

First, convert from hectares to square meters
1 hectare = 10000 meters²
2 hectares =?
2 × 10000 meters² = 20,000 meters²
Thus 2 hectares = 20,000 meters²

2. Convert 3 sq. km to square hectometer.

Solution:

First convert from kilometers to square hectometers.
1 km = 10 hm
3 km = ?
1 km² = 100 hm²
Therefore 3 km² = 3 × 100 hm² = 300 hm²

3. Convert 4 hectares in ares?

Solution:

Convert from hectares to ares.
1 hectare = 100 ares
4 hectares =?
4 hectares = 4 × 100 ares
Thus 4 hectares = 400 ares

4. Convert from 50 sq. cm to mm²

Solution:

Convert from cm² to mm²
1 cm = 10mm
1 cm² = 10 × 10 mm² = 100 mm²
50 cm² = 50 × 100 mm² = 5000 mm²
Thus, 50 cm² = 5000 mm²

5. Convert 50 kilometers to meters?

Solution:

Convert from kilometers to meters.
1 km = 1000 meters
50 km =?
50 × 1000 meters = 50,000 meters
Thus 50 km = 50,000 meters

6. Convert 35 square meters to dm²?

Solution:

Convert from square meters to sq. decimeters.
1 m² = 100 dm²
35 m² = 35 × 100 dm²
35 m² = 3500 dm²
Thus 35 m² = 3500 dm²

7. Convert 15 square feet into square meters.

Solution:

First convert square feet into square meters.
1 ft² = 0.09 m²
15 ft² = 15 × 0.09 m² = 1.35 sq. meters
Thus 15 square feet = 1.35 m².

FAQs on Units of Area Conversion

1. How to convert units to other units?

1. Write the units in a fraction
2. Multiply and cancel the units in numerator and denominator.

2. What is a conversion rate?

Conversion rate = total number of conversions/total number of sessions × 100

3. How to convert the conversion factor?

The conversion factor is the number that is used to change the unit either by multiplying or dividing.