Question

A square $ABCD$ and a circle are drawn a graph sheet such that the vertices of the square $ABCD$ are $A(-2,2),B(2,2),C(2,-2),D(-2,-2)$ and the circle with centre $(0,0)$ and radius $2cm$ is cut off from the above square $ABCD$. Find the area of the remaining region in the square $ABCD$.

Answer 1

Since $ABCD$ is a square $AB=BC=CD=DA$

Using distance formula $AB=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

$=\sqrt{{(-2-2)}^2+{(2-2)}^2}=\sqrt{16}=4$units

Area of remaining region $=$Area of square $ABCD-$Area of circle

$={\left(side\right)}^2-\pi r^2$

$={\left(4\right)}^2-\pi {\left(2\right)}^2$

$=\left(16-4\pi \right)c{m}^2$