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

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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.

muyb ajo

step-by-step explanation:

jegosu

10/60

step-by-step explanation:

if you divide 10 by 60 the answer is 0.166666 while if you divide or solve the other problems it equals 0.6