To practice math skills there is no effective way better than practicing using Worksheets. Try solving using the free printable worksheets on area of a square and rectangle and improve your analytical and problem-solving skills. Area of a Square and Rectangle Word Problems has questions on finding areas of grid and normal images, missing sides, etc. Assess your strengths and weaknesses using the Area of a Square and Rectangle Questions and Answers provided and improvise on the areas of need accordingly.
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Area of a Square and Rectangle Questions
Example 1.
Find the area of the square length of whose sides are given below:
1. 17
2. 43
3. 55
4. 8
5. 30
Solution:
1. The area of the square=172
=289
2.The area of the square=432
=1849
3.The area of the square=552
=3025
4.The area of the square=82
=64
5.The area of the square=302
=900
Example 2.
Fill in the blanks
Length Breadth Area
1. 6 cm 5 cm ______
2. 7 cm 3 cm _______
3. 9 cm 4 cm ________
4. 5 cm _____ 10 sq cm
5. 15 m ______ 150 sq m
Solution:
1. Area=length × breadth=6 × 5=30 sq cm
2. Area=7×3=21 sq cm
3. Area=9 × 4=36 sq cm
4. Length=5 cm
Area=10 sq cm
Breadth=10/5=2
Hence, the breadth of the rectangle=2.
5. Length=15 m
Area=150 sq m
breadth=150/15=10 sq m
Hence, the breadth of the rectangle=10.
Example 3.
Find the area of the following
1. The side of the square is 12 cm. Find the area?
2. The side of a square is 19 cm. Find the area?
3. Rectangle of length 13 cm and breadth 3 cm. Find the Area?
4. Rectangle of length 17 cm and breadth 4 cm. Find the Area?
Solution:
1. The side of the square =12 cm
Area of the square=122=144
2. The side of the square=19 cm
Area of the square=192=361
3. Length of a rectangle=13 cm
The breadth of a rectangle=3 cm
Area of the rectangle=13 × 3=39
4. Length of the rectangle=17 cm
The breadth of the rectangle=4 cm
Area of the rectangle=17×4=68
Example 4.
The bed is 6 m long and the width is 5 m. Find the area occupied by the bed?
Solution:
The length of the bed=6 m
The breadth of the bed=5 m
Area of the bed=6×5=30 sq m
Hence, the Area occupied by the bed=30 sq m.
Example 5.
Suresh wants a new carpet for the rectangular function hall. Hall is in a rectangular shape of length 19 cm and width 10 cm. Find the area of the carpet that covers the entire hall?
Solution:
Length of the hall=19 cm
width of the hall=10 cm
Area of the carpet that covers the entire hall=19 × 10=190 sq cm.
Hence, the area of the carpet is 190 sq cm.
Example 6.
The area of the square-shaped artificial grass is 4900. Find the length of the side of the grass?
Solution:
The area of the square-shaped artificial grass=4900
Length of side of grass=\(\sqrt{ 4900 }\)
=70
Hence, the length of the square-shaped artificial grass is 70.
Example 7.
Find the area of the carpet whose perimeter is 60?
Solution:
The perimeter of the square=60
We know that the perimeter of the square=4 × side
Therefore, 4 × side=60
side=60/4=15
Hence, the area of the carpet is 15.
Example 8.
The perimeter of the square garden is 164 m. Find the cost of fencing it at the rate of 10 per m2?
Solution:
The perimeter of the square garden=164
Therefore, the side of the square-shaped garden=164/4=41
Therefore, the area of the square-shaped garden=41× 41 m2=1681 m2
For 1 m2, cost of fencing=10
For 1681 m2, cost of fencing=1681 × 10=Rs16810 m2
Hence, the cost of fencing for 1681 m is Rs16810.
Example 9.
Find the breadth of the rectangular plot of land whose area is 740 m and whose length is 15. Find its perimeter?
Solution:
The area of the rectangular plot of land=740 m
The length of the rectangular plot of land=15 m
The breadth of the rectangular plot of land=740/15=49
The perimeter of the rectangular plot is=2(length+breadth)
=2(15+49)
=2(64)=128 sq m
Hence, the perimeter of the rectangular plot is 128 sq m.
Example 10.
The length and breadth of the rectangular courtyard are 60 m and 22 m. Find the cost of leveling it at the rate of Rs 10 per m2. Also, find the distance covered by the Ram to take 3 rounds of the courtyard?
Solution:
The Length of the courtyard=60 m
The breadth of the courtyard=22m
The perimeter of the courtyard=2(60+22)
=2(82)
=164 m
Distance covered by the Ram to take 3 rounds=3 × 164=492 m
Area of the courtyard=60 × 22=1320 sq m
For 1 m2, the cost of levelling= Rs 10
For 1320, the cost of leveling =1320 × 10=Rs 13200.
Hence, the cost of leveling is Rs 13200 and the distance covered by Ram to take 3 rounds is 492 m.