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In the figure below, isosceles triangle ABC with base AB has altitude CH = 24 cm, DE = GF, HF = 12 cm, and FB = 8 cm. find area of CDEFG

 

 Oct 25, 2021
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Think about using similiar triangles. Notice how triangle CHB is similiar to GFB therefore we can set up a ratio like so to find the length of GF:

 

\(\frac{CH}{GF} = \frac{HB}{FB}, \frac{24}{20} = \frac{GF}{8}, GF = 9.6.\)

 

Therefore, we know that the area of GFB = 9.6 * 8 divided by 2. Therefore, GFB = 38.4.

 

Via symmetry, we know that DAE = 38.4. Therefore, the area of CDEFG = (area of entire triangle) - 38.4 * 2 = 480 - 76.8 = 403.2

 Oct 25, 2021

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