Find the area of the shaded region. Round answers to the nearest tenth. Assume all inscribed polygons are regular.Select one:a. 29.3 units2b. 19.5 units2c. 23.7 units2d. 26.1 units2
Accepted Solution
A:
Answer:a. 29.3 units²Step-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) / rb = 2r sin 36°And:cos 36° = h / rh = 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 units²Three fifths of the area is shaded, so:⅗ A ≈ 29.3