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Inscribed square in a circle

This math skill demonstrates how to find the area of a circle in which a square is inscribed. It involves calculating the side length of the square, using it to determine the radius of the circle through Pythagorean theorem, and then using the radius to compute the circle's area.

Learn inscribed square in a circle

Teaching Transcript

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Find the area of the circle that this square is inscribed in

We know the area of the square is 16, so its side length must be 4

So the distance from the center to the edge is half of that, or 2

And similarly, the distance from that half way point to the corner is also 2

So we have a right triangle with legs that are both 2

So by Pythagoras, the hypotenuse, which is also the radius of the circle is root 8

If the radius is root 8, then the area is 8 pi

Skill Practice

Inscribed square in a circle

Test your understanding of inscribed square in a circle by practicing it! Work through the below exercises to use it in practice.