In the figure below, isosceles triangle ABC with base AB has altitude CH = 24 cm. , DE = GF, HF = 15 cm, and FB = 3 cm. What is the number of square centimeters in the area of pentagon CDEFG?
Triangle CHB is similiar to triangle GFB by angle angle similarity (shared angle B and right angle).
Thus, the ratio of CH to GF is 18:3 or 6:1. Since CH is 24, then GF is 4.
If GF is 4, then the area of triangle GFB is 6. The area of triangle ADE is also 6. To calculate the area of the pentagon, just calculate the area of the entire trianglce ABC and subtract it by ([ADE] + [GFB]). The area of triangle ABC is 36 x 24 / 2 = 432 units^2.
Thus, the area of pentagon CDEFG is 420 units^2.