Question

The figures below are based on semicircles and squares. Find the perimeter and the area of each shape. Give your answer as a completely simplified exact value in terms of π (no approximations). Thanks! :)

Answer 1

area of square is 36 cm sq.

perimeter of square is 24 cm

Area of large semicircle is 18π cm sq.

Area of small semicircle is 4.5π cm sq.

Perimeter of large semicircle is 6π cm

Perimeter of small semicircle is 3π cm

Step-by-step explanation:

Square:

Area of square= a^2

The side of the square, (a)= 6 cm

Area= 6*6= 36 cm sq.

perimeter of square= 4a =4*6 =24 cm

Large semicircle:

Radius of large semicircle (r)= 6 cm

Area of semicircle= (πr^2)/2 =36π/2 =18π cm sq.

Perimeter of semicircle= (2πr)/2 =(2*π*6)/2 = 6π cm

Small semicircle:

Radius of small semicircle (r)= 3 cm

Area of semicircle= (πr^2)/2 =9π/2 =4.5π cm sq.

Perimeter of semicircle= (2πr)/2 =(2*π*3)/2 = 3π cm