+4609 \(ABCDEFGH\) is a regular octagon of side 12cm. Find the area in square centimeters of trapezoid \(BCDE\). Express your answer in simplest radical form.
+128631 This is an isosceles trapezoid...angle DEB = 45°
We can find the height, H, of the tapezoid as
sin(45) = H / 12
12 sin (45) = H
6√2 cm = H
And the longer base length is [12 + 6√2 + 6√2] = [ 12 + 12√2 ] cm
So....the area is
height * (sum of base lengths) / 2 =
6√2 [ 12 + (12 +12√2) ] / 2 =
6√2 [ 24 + 12√2 ] / 2 =
3√2 [ 24 + 12√2] =
72√2 + 72 =
72 (√2 + 1) cm^2
