Question

In the diagram $\square ABCD$ is the rectangular paper. If $AB=20cm$ and $BC=14cm$ then ______ is the area of the shaded region if the semicircle with diameter $BC$ is cut from the paper.

• A. $200$
• B. $203$
• C. $213$
• D. $208$

Answer 1

The correct option is B $203$

$\square ABCD$ is a rectangle.
$AB=20cm$
$BC=14cm$.

$\therefore$ Area of a rectangle $=AB\times BC$
$=20\times 14$
$=280c{m}^2$

Area of semicircle with diameter $\overline{BC}$
$=\frac{\pi r^2}{2}$
$=\frac{22}{2\times 7}\times {\left(\frac{14}{2}\right)}^2(\because r=\frac{BC}{2})$
$=77c{m}^2$

$\therefore$ The area of shaded region
$=(280-77)c{m}^2$
$=203c{m}^2$.