Area of a Circle Inscribed in a Square

Question

A circle is inscribed in a square. The diameter of the circle is 12.4 mm. Find the area of the region that is outside of the circle and inside the square. Round the answer to the nearest tenth.

Answer 1

The area that is outside the circle and yet inside the square is,

$$A_{square} - A_{circle}$$ $$d^2 - \pi r^2$$

Since $r = d/2$,

$$d^2 - \pi (\frac{d}{2})^2$$

Since $d = 12.4mm$, calculate

$$(12.4mm)^2 - \pi (\frac{12.4mm}{2})^2$$ $$=32.997mm^2$$

Answer 2

Hint: the diameter of the circle equals to the side length of square.

$$S_{\text{circle}} = \dfrac{\pi d^2}{4}$$ $$S_{\text{square}} = a^2$$ $$12.4^2 - \dfrac{\pi 12.4^2}{4} = 12.4^2(1 - \dfrac{\pi}{4}) = 153.76\cdot\dfrac{0.86}{4}$$

Answer 3

It's simply the area of your square minus the area of your circle.

Answer 4

diameter of circle = side of square.

therefore if a =side of square side = 12.4

therefore a=12.44

then area of circle = piD^2/4=120.763

area of square = a^2 =154.7536

there difference = 34=30mm^2