Question

A circle is drawn within a square as shown. What is the best approximation for the area of the shaded region? Use 3.14 to approximate pi.

Answer 1

The best approximation for the area of the shaded region is 21.5 cm²

Explanation:

Area of the shaded region is equal to the area of the square minus the area of the circle

Let us find the area of the square and the area of the circle

• The formula of the area of a square is A = s², where s is its side
• The formula of the area of a circle is A = πr², where r is its radius

∵ The circle touch the 4 sides of the square

∴ The length of the diameter of the circle is equal to the

length of the side of the square

∵ The length of the side of the square = 10 cm

∴ The length of the diameter of the circle = 10 cm

∵ Area of the square = s²

∵ s = 10 cm

∴ Area of the square = (10)²

∴ Area of the square = 100 cm²

∵ The radius of a circle is half its diameter

∵ The diameter of the circle = 10 cm

∴ The radius =
`(1)/(2)` × 10 = 5 cm

∴ The area of the circle = πr²

∴ The area of the circle = 3.14(5)²

∴ The area of the circle = 78.5 cm²

Now let us find the shaded area

∵ The shaded area = area of the square - area of the circle

∴ The shaded area = 100 - 78.5

∴ The shaded area = 21.5 cm²

The best approximation for the area of the shaded region is 21.5 cm²