Inscribed Circle in Square - Circle Area to Square Side Length

Level 1

This math topic focuses on finding the side length of a square when given the area of an inscribed circle. It is part of an introductory unit on inscribed squares and circles. The problems are structured to require using the relationship between the diameter of the circle and the side length of the square, along with the formula for the area of a circle. Different area values are given across several problems, and students are tasked with deriving the side length through various options presented using mathematical expressions, promoting understanding of geometric relationships and algebraic manipulation.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Inscribed Circle in Square - Circle Area to Square Side Length Worksheet

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Inscribed Circle in Square - Circle Area to Square Side Length
1
Find the side length of a square that has an inscribed circle of area 3
An svg image showing a math problem
a A LaTex expression showing 2square root of 3 over Pi
b A LaTex expression showing {18 over 2 } to the power of 2 Pi
c A LaTex expression showing 2square root of 1 over Pi
d A LaTex expression showing 9Pi
e A LaTex expression showing 4square root of 6
2
Find the side length of a square that has an inscribed circle of area 5
An svg image showing a math problem
a A LaTex expression showing 2square root of 25 over 2Pi
b A LaTex expression showing 2square root of 2 over Pi
c A LaTex expression showing 10 over Pi
d A LaTex expression showing 2square root of 50 over 2Pi
e A LaTex expression showing 2square root of 5 over Pi
f A LaTex expression showing 25 over Pi
3
Find the side length of a square that has an inscribed circle of area 6
An svg image showing a math problem
a A LaTex expression showing 72 over Pi
b A LaTex expression showing 2square root of 6 over Pi
c A LaTex expression showing 4square root of 72
d A LaTex expression showing 36 over Pi
e A LaTex expression showing 2square root of 3 over Pi
f A LaTex expression showing 18Pi
4
Find the side length of a square that has an inscribed circle of area 8
An svg image showing a math problem
a A LaTex expression showing 64Pi
b A LaTex expression showing {128 over 2 } to the power of 2 Pi
c A LaTex expression showing {64 over 2 } to the power of 2 Pi
d A LaTex expression showing 2square root of 8 over Pi
e A LaTex expression showing 16Pi
f A LaTex expression showing 2square root of 4 over Pi
5
Find the side length of a square that has an inscribed circle of area 2
An svg image showing a math problem
a A LaTex expression showing 4
b A LaTex expression showing 4 over 2 square root of 2
c A LaTex expression showing 2square root of 1 over Pi
d A LaTex expression showing 2square root of 2 over 2
e A LaTex expression showing {8 over 2 } to the power of 2 Pi
f A LaTex expression showing 2square root of 2 over Pi
6
Find the side length of a square that has an inscribed circle of area 7
An svg image showing a math problem
a A LaTex expression showing 2square root of 14 over 2Pi
b A LaTex expression showing 2square root of 3 over Pi
c A LaTex expression showing 49 over Pi
d A LaTex expression showing 2square root of 7 over Pi
e A LaTex expression showing {25 over 2 } to the power of 2 Pi
f A LaTex expression showing {98 over 2 } to the power of 2 Pi