Answer:
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