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# 2nd geo help!

+1
201
2
+3750

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 $$CDEFG$$?

Feb 23, 2018

### 2+0 Answers

#1
+15375
+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

Feb 23, 2018
#2
+3750
+2

Great sol, EP! I understand it much better, now!

tertre  Feb 23, 2018

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