In the figure below, isosceles \(\triangle ABC\) with base \(\overline{AB}\) has altitude \(CH = 24\) cm. , DE = GF, \(HF = 12\) cm, and \(FB = 6\) cm. What is the number of square centimeters in the area of pentagon \(CDEFG\)?

tertre Feb 23, 2018

#1**+2 **

The area of the WHOLE figure is 1/2 b h = 1/2 ( 36)(24) = 432 cm^2

Now subtract the small right triangles in the corners

- 2 x 1/2 x 6 x FG

via similar triangles

CH/HB = FG/6

24/18 = FG/6

FG = 8

- 2 x 1/2 x 6 x 8 = -48

Pentagon area = 432 - 48 = 384 cm^2

ElectricPavlov Feb 23, 2018