Mensuration Test

Result

Mensuration Test - 1

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Question 1
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If the perimeter of a square is 32 cm while that of a rectangle of length 12 cm is 36 cm, then the area of the

A
rectangle is more than that of the square by 4 cm²

B
rectangle is more than that of the square by 8 cm²

C
square is more than that of the rectangle by 4 cm²

D
square is more than that of the rectangle by 8 cm²

Solution

Let the length of the side of the square be s.

∴ Perimeter of the square = 4 × s = 32 cm
s=32/4=8 cm
∴ Area of the square = s × s = 8 cm × 8 cm = 64 cm²

Length (l) of the rectangle = 12 cm

Let the breadth of the rectangle be b.

∴ Perimeter of the rectangle = 2 × (l + b) = 36 cm

⇒ 12 cm + b = 18 cm

⇒ b = 18 cm − 12 cm = 6 cm

∴ Area of the rectangle = l × b = 12 cm × 6 cm = 72 cm²

Thus, the area of the rectangle is more than that of the square by (72 − 64) cm² = 8 cm².
Question 2
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Use the following information to answer the next question.

A rectangular garden has a length of 18 m and a width of 12 m. The garden is required to be fenced with three rounds of wire.

What is the total length of wire required to fence the garden?

A
30 m

B
60 m

C
120 m

D
180 m

Solution

The length of wire around the field in one round is equal to the perimeter of the garden.

∴ Perimeter of the garden = 2(l + b) [The garden is rectangular]

= 2(18 m +12 m)

= 2 × (30 m) = 60 m

⇒ Total length of wire required = 3 × 60 m = 180 m

Thus, the total length of wire required to fence the garden is 180 m.