ABCDEFGH is a regular octagon of side 12cm. Find the area in square centimeters of trapezoid BCEF.
+1641 https://web2.0calc.com/questions/abcdefgh-is-a-regular-octagon-of-side-12cm
+129899 Let's see how the guest derived his/her answer.....
Look at the following:
The area we seek is (1/2) the area of the octagon less the area of triangle CDE
Note that angle CDE = 135°
Area of triangle CDE = (1/2) (CD) (DE) sin (135) = (1/2) (12) (12) ( 1/ sqrt(2)) = 72/sqrt (2) = 36sqrt (2) [1]
Area of (1/2) of the octagon = ( 1 + sqrt (2) ) * side^2 = (1 + sqrt (2) ) (12)^2 = (1 + sqrt (2) ) (144) =
144 + 144sqrt (2) [2]
Area of trapezoid = [2] - [1] = [ 144 + 108 sqrt (2)] cm^2 ≈ 296.735 cm^2
