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Question 5 (1 point)

Find the area of the shaded region of this regular polygon. (Round to the nearest
hundredth)

Question 5 (1 point) Find the area of the shaded region of this regular polygon. (Round-example-1

1 Answer

1 vote
The polygon is a regular octagon. Each shaded triangle is isosceles, has vertex angle of 360°/8 = 45°, base angles 67.5°, and base = 8.
Height of triangle = 4tan(67.5°)
area of triangle = 0.5(base)(height) = 0.5(8)(4tan(67.5°))
Shaded region = 2*0.5(8)(4tan(67.5°)) = 32tan(67.5°) ≅180.71 cm^2
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