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).

Area of the shaded region = 16(π - 2) in²

Perimeter of the shaded region = 4(π + ) in

Step-by-step explanation:

Since, BDC is a quarter of the circle with radius = 8 in.

Area of the quarter of the circle =

                                                     =

                                                     = 16π in²

Area of ΔBCD =

                        =

                        = 32 in²

Since, area of the shaded part = Area of quarter of the circle - Area of triangle BCD

= (16π - 32)

= 16(π - 2) in²

Therefore, area of the shade region = 16(π - 2) in²

Similarly, length of arc BD =

                                            =

                                            = 4π in.

Length of the diagonal of a square = (Side)√2

                                                          = 8√2 in

Perimeter of the shaded region = Length of arc BD + Length of diagonal BD

= 4π + 8√2

= 4(π + 2√2) in.

1) letter c.

2) 4 square root of 9

hope this

step-by-step explanation: