Make use of this excellent opportunity and practice the questions in the area. You can improve your knowledge regarding the concept of finding areas for different figures. Assess your strengths and weaknesses by solving from the Area Practice Test as a part of your preparation. To make it easy for you we have compiled the step-by-step solutions for all the questions. Download the Practice Test on Area without any further delay and ace up your preparation.
Also, Refer:
- Worksheet on Area of Regular Figures
- Worksheet on Area of a Square and Rectangle
- Word Problems on Area of a Rectangle
Area Questions and Answers
Example 1.
Find the area of a square if the side of the square is 8 cm?
Solution:
Given,
side of the square=8 cm
Area of the square=side × side
=8 × 8=64 sq cm.
Therefore, the area of the square is 64 sq cm.
Example 2.
Find the area of the rectangle of length 13 cm and breadth 8 cm?
Solution:
Given,
The length of the rectangle=13 cm
The breadth of the rectangle=8 cm
Area of the rectangle=Length × breadth
=13 × 8=104 sq cm
Hence, the area of the rectangle is 104 sq cm.
Example 3.
Find the area of the rectangular room of length whose length is 180 m and breadth is 50 m?
Solution:
Given,
The length of the rectangular room=180 m
The breadth of the rectangular room=50 m
Area of the rectangular room=length × breadth
=180 × 50
=9000 sq m
Therefore, the area of the rectangular room is 9000 sq m.
Example 4.
The area of the square field is 121 sq cm. Find the side of the square field?
Solution:
Given,
The area of the square field is=121 sq cm
Area of the square=s × s=s2
121=s2
s2=121
s=\(\sqrt{121}\)
s=11
Hence, the side of the square is 11 sq cm.
Example 5.
The cost of cementing a square yard at Rs 3 per sq meter is 1200. Find the money needed for fencing it at a rate of Rs 6 per meter?
Solution:
Given,
The cost of cementing a square yard at Rs 3 per sq meter is= 1200
Let the side be X m.
Rate of cementing=Rs 3 per sq m
Total cost=1200
Area for cementing=1200/3=400
x2= 400
x=20
The perimeter of the yard=4a
=4(20)
=80 m
Rate of fencing=Rs 6 per meter
The total cost of fencing the square yard is 80 × 6=Rs 480
Therefore, the total money needed for fencing the square yard is Rs 480.
Example 6.
The perimeter of a square is 120 m. Find the area of the square?
Solution:
The perimeter of a square=120 m
4a=120
a=120/4
=30 sq m
Therefore, the area of the square is 30 sq m.
Example 7.
Find the length of the rectangular garden whose area is 450 sq cm and breadth is 50 cm?
Solution:
Area of the rectangular garden=450 sq cm
The breadth of the rectangular garden=50 cm
The length of the rectangular garden=450/50
=9 cm
Therefore, the length of the rectangular garden is 9 cm.
Example 8.
A square with a side of 6 cm and a rectangle with a width of 3 cm has the same area. what’s the length of the rectangle?
Solution:
area of the square=62
=36 sq cm
The width of the rectangle=3 cm
l ×3=36 sq cm
l=36/3=12 sq cm
Hence, the length of the rectangle is 12 sq cm.
Example 9.
A square with a side of 5 cm and a rectangle with a width of 5 cm has the same area. What is the length of the rectangle?
Solution:
The area of the square is=52=25
The width of the rectangle=5 cm
l ×5=25
l=25/5=5
Hence, the length of the rectangle is 5 cm.
Example 10.
Find the cost of painting a square board of side 49 cm at the rate of Rs 5 per sq cm?
Solution:
Given
side of a square=49 cm
Area of the square=side × side=(49)2
=2401 sq cm
The cost of painting the square board at a rate of Rs 5 per sq cm is
2401 × 5=Rs12005
Therefore, the cost of painting the square board is Rs. 12005.