Question

This figure is made from a part of a square and a part of a circle.
What is the perimeter of this figure, to the nearest unit?
What is the area of this figure, to the nearest square unit?

Answer 1

Given:

The figure is made from a part of a square and a part of a circle

To find:

(1) What is the perimeter of this figure, to the nearest unit?

(2) What is the area of this figure, to the nearest square unit?

Solution:

Please refer to the figure attached below

(1). Finding the perimeter of the given figure:

Arc length, ED = $\frac{\theta}{360} \times 2\pi r = \frac{90}{360} \times 2\times \frac{22}{7} \times 5 = 7.85\: units$

Therefore,

The perimeter of the given figure is,

= AC + CD + ED + EF + AF

= 10 + 5 + 7.85 + 5 + 10

= 37.85 units

rounding off to the nearest unit

≈ 38 units

Thus, the perimeter of the given figure is → 38 units.

(2). Finding the area of the given figure:

Area of the sector, HED = $\frac{\theta}{360} \times \pi r^2 = \frac{90}{360} \times \frac{22}{7} \times 5^2 = 19.64\: units^2$

Area of the square, ABHG = 5² = 25 units²

Area of the square, BCDH = 5² = 25 units²

Area of the square, EFGH = 5² = 25 units²

Therefore,

The area of the given figure is,

= Area(HED) + Area(ABHG) + Area(BCDH) + Area(EFGH)

= 19.64 + 25 + 25 + 25

= 94.64 units²

rounding off to the nearest square unit

≈ 95 units²

Thus, the area of the given figure is → 95 units².

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