How do you find the circumference and area of a circle that has a rectangle inscribed inside it with sides that are 9 by 12?

May 21, 2018

See below

Explanation:

If rectangle is inscribed inside, then his diagonals are diameters of circle. Applying Pithagorean theorem we have

${d}^{2} = {9}^{2} + {12}^{2} = 81 + 144 = 225$

$d = 15$

Then radius is $r = \frac{d}{2} = 7.5$

The circunference is $L = 2 \pi 7.5 = 15 \pi$ length units

And Area $S = \pi {7.5}^{2} = 56.25 \pi$ square units