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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

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Find the side length of a square that has an inscribed circle of area 4

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

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Math worksheet on 'Inscribed Circle in Square - Circle Area to Square Side Length (Level 1)'. Part of a broader unit on 'Inscribed Squares and Circles - Intro' Learn online: app.mobius.academy/math/units/inscribed_squares_and_circles_intro/
1
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 18
b A LaTex expression showing 2square root of 6 over Pi
c A LaTex expression showing 72 to the power of 2 over 2 Pi
d A LaTex expression showing {18 over 2 } to the power of 2 Pi
e A LaTex expression showing 2square root of 72 over 2Pi
f A LaTex expression showing 72Pi
2
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 49Pi
b A LaTex expression showing 25 over Pi
c A LaTex expression showing 25Pi
d A LaTex expression showing {(square root of 49)} to the power of 2 Pi
e A LaTex expression showing 4square root of 98
f A LaTex expression showing 2square root of 7 over Pi
3
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 over Pi
b A LaTex expression showing 4 over 2 square root of 2
c A LaTex expression showing 4 over Pi
d A LaTex expression showing 2square root of 2 over Pi
e A LaTex expression showing {8 over 2 } to the power of 2 Pi
f A LaTex expression showing 4 over Pi
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 16 to the power of 2 over 2 Pi
b A LaTex expression showing 2square root of 64 over 2Pi
c A LaTex expression showing 32 over Pi
d A LaTex expression showing {32 over 2 } to the power of 2 Pi
e A LaTex expression showing 2square root of 8 over Pi
f A LaTex expression showing 16
5
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 2square root of 18 over 2
c A LaTex expression showing 6
d A LaTex expression showing 18 to the power of 2 over 2 Pi
e A LaTex expression showing 6 over 2 square root of 2
f A LaTex expression showing 9 over Pi
6
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 {10 over 2 } to the power of 2 Pi
b A LaTex expression showing 2square root of 5 over Pi
c A LaTex expression showing {(square root of 25)} to the power of 2 Pi
d A LaTex expression showing 50 to the power of 2 over 2 Pi
e A LaTex expression showing 4square root of 10
f A LaTex expression showing 2square root of 50 over 2
7
Find the side length of a square that has an inscribed circle of area 4
An svg image showing a math problem
a A LaTex expression showing 16Pi
b A LaTex expression showing 4square root of 8
c A LaTex expression showing 8 to the power of 2 over 2 Pi
d A LaTex expression showing 8 over Pi
e A LaTex expression showing 16 over Pi
f A LaTex expression showing 2square root of 4 over Pi