Find the area and the perimeter of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations). The figures below are based on semicircles or quarter circles.

Area = 8(π + 5) cm²

Perimeter = 2(2π + 11) cm

Step-by-step explanation:

The figure above is composed of a triangle and a semicircle.

Area = area of semicircle + area of triangle

Area = (½πr²) + (½*b*h)

Where,

r = radius = ½ of 8 = 4cm

b = base = 8 cm

h = height = 10 cm

Area = (½*π*4²) + (½*8*10)

Area = (½*π*16) + (4*10)

Area = 8π + 40

Area = 8(π + 5) cm²

Perimeter = perimeter of semicircle + sum of the sides of the triangle.

Perimeter of semicircle = πr = π*4 = 4π cm

One side of the triangle can be calculated using Pythagorean theorem as follows:

Let the side be x.

x² = 10² + 4²

x² = 100 + 16

x² = 116

x = √116 = 10.77 ≈ 11

Sum of both sides = 11+11 = 22cm

Perimeter of the figure = 4π + 22

Perimeter = 2(2π + 11) cm