# Practice Test on Area and Perimeter of Square | Questions on Area and Perimeter of Square

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.