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

40 + 8pi

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

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

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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step-by-step explanation: