Question

In the figure given below, $ABCD$ is a rectangle, $AB=14cm,BC=7cm$. From the rectangle, a quarter circle $BFEC$ and a semicircle $DGE$ are removed. Calculate the area of the remaining piece of the rectangle. (Take $\pi =\frac{22}{7}$)

Answer 1

Area of rectangle $ABCD=14\times 7=98c{m}^2$
Area of quarter circle $BFEC=\frac{1}{4}\pi (7{)}^2=\frac{49}{4}\pi$
Area of semi-circle $DGE=\frac{1}{2}\pi {\left(\frac{7}{2}\right)}^2=\frac{1}{2}\times \frac{49}{4}\pi$
Area of remaining piece of rectangle $=98-[\frac{49}{4}\pi +\frac{1}{2}\times \frac{49}{4}\pi ]$
$=98-\frac{49}{4}\pi [1+\frac{1}{2}]$
$=98-\frac{49}{4}\times \frac{22}{7}\times \frac{3}{2}=98-\frac{231}{4}$
$=98-57.75$
$=40.25c{m}^2$.