Question

A square is circumscribed about a circle with a diameter of 10 cm. What is the correct set up to find the area of the shaded region?

Answer 1

21.5 cm² (nearest tenth)

Explanation:

Formulae

• Area of a square = x² (where x is the side length)
• Area of a circle = πr² (where r is the radius)
• Radius = 1/2 diameter

Solution

To find the shaded region, subtract the area of the circle from the area of the square.

Square

Area of the square = 10² = 100 cm²

Circle

Given diameter of circle = 10 cm

⇒ radius = 10 ÷ 2 = 5 cm

⇒ Area of the circle = π · 5² = 25π cm²

Area of shaded region

= area of square - area of circle

= 100 - 25π

= 21.46018366...

= 21.5 cm² (nearest tenth)