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  S1=πr2 r2=S1/π=216/π=68.755 r2=a2/4+b2/4 4r2=a2+b2 b2=4r2−a2=4⋅68.755−52 b=15.812  S=ab=5⋅15.812=79.06a = 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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Pythagorean theorem is the base for the right triangle calculator.
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