Area of a Square

Geometry Level 2

The total area covered by the red circles is 20 π 20\pi . What is the area of the large square? (All circles are congruent and tangent to each other or to the side of the side of the square.)


The answer is 144.

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1 solution

Hana Wehbi
Dec 18, 2018

Note that if we draw a line segment connecting the centers of the circles, we get the length of this segment equals to triple the diameter of one circle.

The area of the five circles is 20 π 20\pi , thus the area of one circle is 4 π = π × r 2 r 2 = 4 d = 4 4\pi =\pi\times r^2\implies r^2=4\implies d=4 .

The measure of the side of the square is 4 × 3 = 12 s 2 = 144 4\times 3=12 \implies s^2=144 which is the area of the square.

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