Question

Calculate the shaded region

Answer 1

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First find the area of the sector.

For that, use this equation:

area = $\frac{x }{360} * \pi r^{2}$

where 'x' is the angle and 'r' is the radius

Sub the values in

area = $\frac{56}{360} * \pi15^2$

Solve:

area = $35\pi$

It is easier to keep it in terms of pi until the end

Now, calculate the area of the triangle within the sector

area = 1/2 ab x sinC

where 'a' and 'b' are the radius (side lengths) and C is the angle

thus,

area = 1/2(15 x 15) x sin(56)

area = 93.27 (to 2 d.p)

Now subtract the area of the triangle from the area of the sector

$35\pi$ - 93.27 = 16.6857

This would give you a final answer of 16.69 units^2

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