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.