Answer:
(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
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* 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.
