Question

Can someone please help me?? Im not quite sure how to get this answer.

Answer 1

Answer:

C. 54π + 20.25√3 cm²

Step-by-step explanation:

The shaded area can be split into two areas: a sector and an isosceles triangle.

Area of a sector is:

A = (θ/360°) πr²

where θ is the central angle and r is the radius.

Area of an isosceles triangle can be found with SAS formula:

A = ½ ab sin θ

where a and b are two sides of a triangle and θ is the angle between them.

In this case, r = a = b = 9 cm.  The central angle of the sector is 240°, and the vertex angle of the triangle is 120°.  Therefore, the total area is:

A = (240°/360°) π (9 cm)² + ½ (9 cm) (9 cm) sin 120°

A = 54π + 20.25√3 cm²