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Inscribed circle in a square

The math skill being taught is how to find the area of a square when a circle is inscribed within it by using the circle’s area to determine its radius, doubling the radius to find the diameter (which equals the side of the square), and then determining the area of the square.

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Teaching Transcript

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

The circle has an area of 9 pi, and the area of a circle is given by pi times the radius squared. So the radius squared must be 9, and the radius must be 3

If the radius is 3, then the diameter is twice that, or 6

Since the circle is inscribed, the diameter crosses the full square, so the square's width and height are both 6

So the square's area is 6 times 6, or 36

Skill Practice

Inscribed circle in a square

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