Find the area of the shaded region. round answers to the nearest tenth. assume all inscribed polygons are regular.
select one:
a. 29.3 units2
b. 19.5 units2
c. 23.7 units2
d. 26.1 units2

a. 29.3 units²

Step-by-step explanation:

The area of a circle is A = πr².

The area of each triangle is A = ½bh.

The vertex angle of each triangle is 360/5 = 72°.  If we cut the triangle in half, we can use trig to write:

sin 36° = (½b) / r

b = 2r sin 36°

And:

cos 36° = h / r

h = r cos 36°

Substituting, we get the area of each triangle is:

A = r² sin 36° cos 36°

A = ½ r² sin 72°

The radius of the circle is 8.  So the area of the circle minus the area of the 5 triangles is:

A = π (8)² − 5 (½) (8)² (sin 72°)

A ≈ 48.9 units²

Three fifths of the area is shaded, so:

⅗ A ≈ 29.3