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=17^{2}

=289

2.The area of the square=43^{2}

=1849

3.The area of the square=55^{2}

=3025

4.The area of the square=8^{2}

=64

5.The area of the square=30^{2}

=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=12^{2}=144

2. The side of the square=19 cm

Area of the square=19^{2}=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 m^{2}?

**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 m^{2}=1681 m^{2}

For 1 m^{2}, cost of fencing=10

For 1681 m^{2}, cost of fencing=1681 × 10=Rs16810 m^{2}

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 m^{2}. 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 m^{2}, 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.