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Printjmc
geometry senior
Problem
In , , and . Points and lie on and , respectively, with . Points and are on so that and are perpendicular to . What is the area of pentagon ? Express your answer as a common fraction.
Solution
Because , , and are similar right triangles whose hypotenuses are in the ratio , their areas are in the ratio .
The area of is , so the areas of and are and , respectively.
Thus the area of pentagon is .
The area of is , so the areas of and are and , respectively.
Thus the area of pentagon is .
Final answer
\frac{240}{13}