Find the area of the shaded regions below. give your answer as a completely simplified exact value in terms of π (no approximations).

  (8π -8√3) cm²

Step-by-step explanation:

The area of a circle with radius 4 cm is given by ...

  A = πr² = π(4 cm)² = 16π cm².

The red shaded portion is part of a semicircle. That semicircle will have an area half that of the circle, so ...

  A/2 = 8π cm²

__

The triangle OCB is an equilateral triangle, so the angle at B is 60°. The side AC is then √3 times side BC*, so is 4√3 cm. The area of triangle ABC is then ...

  A = (1/2)AC·BC = (1/2)(4√3 cm)(4 cm) = 8√3 cm²

This area is subtracted from that of the semicircle to obtain the red shaded area:

  red area = semicircle area - triangle area

  red area = (8π -8√3) cm²

* AC can be found either from the Pythagorean theorem (√(8²-4²)), using trig functions (4tan(60°)), or using your knowledge of 30°-60°-90° triangles.

hows it hangin lol

step-by-step explanation:

all the angles opposite to the angle 150 would be 150 and all the angles that are next to 150 are 30 because they equal 180 it you add it up.

step-by-step explanation: