ABCDEFGH is a regular octagon of side 12cm. Find the area in square centimeters of trapezoid \(BCEF\).
+130071 See the image below (not to scale)
The area of (1/2) of the octagon = (1/2) [ 2 * 12^2 ( 1 + sqrt 2)] = 144 (1 + sqrt 2)
Triangle CDE has an area of (1/2) CD * DE * sin 135° = (1/2) 12^2 sin 135° = 72 / sqrt 2 = 36sqrt (2)
So the area of the trapezoid BCEF =
area of (1/2) octagon - area of triangle CDE
144 ( 1 + sqrt 2) - 36 sqrt 2 =
[144 + 108sqrt 2] cm^2 ≈ 296.74 cm^2
