Shaded Region – Circle Inscribed in a Square

A circle with radius 3 cm is inscribed in a square.

circle inscribed in a square

Find the area of the shaded region. Let pi = 3.14 and round your answer to the nearest tenths.


We know that

area of shaded region = area of square – area of circle 

We find the area of the square and the circle. The diameter of the circle is 6 cm. This is the same as the length of the square.

area of the square = 6 cm × 6 cm

area of the square = 36 sq. cm.

area of the circle = pi × r × r

area of a circle = 3.14 × 3× 3

area of the circle = 28.26 sq. cm.

Now, we find the area of the shaded region.

area of shaded region = 36 – 28.26 = 7.74 sq. cm.

Rounding to the nearest tenths, the final answer is 7.7 sq. cm.

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