Question

a triangle is placed in a semicircle with a radius of 4cm, as shown below. Find the area of a shaded region. Use the value of 3.14 for pi, and do not round your answer. Be sure to include correct unit in your answer.

Answer 1

9.12 cm²

Explanation:

You want the area of the two segments outside an isosceles triangle inscribed in a semicircle of radius 4 cm.

Segment area

The area of a segment of a circle is ...

A = 1/2(r²)(θ -sin(θ)) . . . . . θ is the measure of the central angle in radians

Here, we have two congruent segments, each of which has a central angle of 90° = π/2 radians. The radius is 4 cm, so the areas total ...

A = 2(1/2)(4 cm)²(π/2 -sin(π/2))

A = 16(3.14/2 -1) cm² = 9.12 cm²

The shaded area is 9.12 cm².

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