Question

The figures below are semicircles and squares. Find the perimeter and the area of each shape. Give your answer as a completely simplified exact value in terms of pi (no approximations). Please give both area and perimeter.

Answer 1

Explanation:

Perimeter of a semicircle = 0.5πd.

Perimeter of big semicircle = (0.5)(π)(18cm) = 9πcm

Perimeter of 3 small semicircles = (1.5)(π)(6cm) = 9πcm

Hence total perimeter = 9πcm + 9πcm = 18πcm.

Area of a semicircle = 0.5πr²

Area of big semicircle = (0.5)(π)(9cm)² = 40.5πcm²

Area of 3 small semicircles = (1.5)(π)(3cm)² = 13.5πcm².

Hence total area = 40.5πcm² + 13.5πcm² = 54πcm².