# Inscribed rectangle

The circle area is 216. Determine the area of inscribed rectangle with one side 5 long.

Result

S =  79.06

#### Solution:

$a = 5 \ \\ \ \\ S_1 = \pi r^2 \ \\ r^2 = S_1/ \pi = 216/\pi = 68.755 \ \\ r^2 = a^2/4 + b^2/4 \ \\ 4 r^2 = a^2 + b^2 \ \\ b^2 = 4 r^2 - a^2 = 4 \cdot 68.755 - 5^2 \ \\ b = 15.812 \ \\ \ \\ S = ab = 5 \cdot 15.812 = 79.06$

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