Question

The figures below are made out of circles, semicircles, quarter circles, and a square. Find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations). Chapter Reference a Answer: A = cm2, P = cm

Answer 1

Answer:

Area of the figure = 31.25π cm²

Perimeter of the figure = (12.5π + 10) cm

Step-by-step explanation:

Area of the given figure = Sum of area of the two semicircle + area of a quarter circle

Area of one quarter circle (CDE) = $\frac{1}{4}(\pi r^{2})$

                                                      = $\frac{1}{4}\pi (5)^2$

                                                      = 6.25π

Area of one semicircle = 2 × Area of one quarter circle

                                      = 2(6.25π)

                                      = 12.5π

Area of the given figure = 2×12.5π + 6.25π

                                        = 25π + 6.25π

                                        = 31.25π cm²

Perimeter of the figure = Perimeter of two semicircles + perimeter of one quarter circle + measure of radius DE + measure of radius AB

Perimeter of one semicircle = πr

                                              = 5π cm

Perimeter of one quarter circle = 2.5π

Perimeter of the complete figure = 10π + 2.5π + 5 + 5

                                                       = (12.5π + 10) cm