If the radius of a circle is decreased by 50%, find the percentage decrease in its area.

Let original radius = R. 

New radius =  $\frac{50}{100}R$=  $\frac{50}{100}R$ 

Original area = $\frac{R}{2}$  and new area =  $\mathrm{\pi R}2$

$\frac{3\mathrm{\pi R}2}{4}*\frac{1}{\mathrm{\pi R}}*100$ 

Decrease in area =  $\pi \frac{R}{2}2=\frac{\mathrm{\pi R}}{2}$ = 75%