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

Find the area of the shaded regions below Give your answer as a completely simplified exact value in terms of π no approximations class=

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Answer: 40 + 8pi

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Work Shown:

Area of triangle ABC = 0.5*base*height

Area of triangle ABC = 0.5*8*10

Area of triangle ABC = 4*10

Area of triangle ABC = 40

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AB = diameter of semi-circle = 8 cm

r = radius

r = half the diameter = AB/2 = 8/2 = 4

So r = 4 is used to find the area of the semi circle

Area of semi-circle = 0.5*(area of whole circle)

Area of semi-circle = 0.5*(pi*r^2)

Area of semi-circle = 0.5*pi*4^2

Area of semi-circle = 0.5*pi*16

Area of semi-circle = 0.5*16*pi

Area of semi-circle = 8pi

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To get the total area, we add the two individual areas. We cannot combine the two terms as 40 and 8pi aren't like terms. So we just leave it as 40+8pi

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