Answer:
Step-by-step explanation:
Divide 360 by the number of sides in a regular polygon to find θ
θ = 360/5 = 72°
Use law of cosines to find the radius of the circle which equals the common length sides of the isosceles triangle
12² = R² + R² - 2•R•Rcos72
12² = 2R² - 2R²cos72
12² = 2R²(1 - cos72)
R² = 12² / 2(1 - cos72)
R² = 104.1993788...
R = 10.2078...
The height of the isosceles triangle is
h = Rcos(θ/2) = 10.2078cos(72/2) = 8.258291...
The shaded area is the area of the circle minus the area of the pentagon.
A = π(104.1993) - 5(½(12)(8.258291))
A = 327.35200... - 247.74874...
A = 79.6032575...
A = 79.60 units²
