Question

For the figures below, assume they are made of semicircles, quarter circles and squares. For each shape, find the area and perimeter. Give your answer as a completely simplified exact value in terms of π (no approximations).

Answer 1

The area of the given figure is 576 cm sq.

The perimeter of the given figure is 96 cm.

Step-by-step explanation:

The shape consists of one semicircle and one square which is cut by a semicircle.

To find Area:

Find the area of semicircle= (πr^2)/2

where r is the radius= diameter/2= 24/2= 12 cm

Area of semicircle= π(12)(12)/2= 144π/2= 72π cm sq.

Find the area of square= a^2

where a is the side of square, a=24 cm.

Area of the square= 24*24= 576 cm sq.

To find the total area of the given figure,

Area of the figure= Area of semicircle+(area of square- area of semicircle)

                             = 72π+576-72π =576 cm sq.

To find perimeter:

Perimeter of semicircle= (2πr)/2

                                       = (2*12*π)/2= 12π cm

Perimeter of square= 4a =4*24 =96 cm

Perimeter of the given figure=  perimeter of semicircle+(perimeter of                        square- perimeter of semicircle)

                                                 = 12π+96+12π =96 cm.