Similar Pentagon Areas Part 1
Let a pentahat be a pentagon with the following properties:
- Two adjacent right angles.
- All sides congruent.
If the area of a pentahat is , where is the length of one of the sides, and , , and are positive integers with square-free, find .
The answer is 8.
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1 solution
Given a pentagon with two right angles and all congruent sides we have a square with an equilateral triangle on top.
The area of the square = s^2
The area of the triangle = sqrt(3)*s^2/4.
Total area = s^2 + sqrt(3)*s^2/4 = s^2 * (1 + sqrt(3) / 4)
a + b + c = 1 + 3 + 4 = 8