Question

Find the perimeter of the shaded region, where $ADC,AEB$ and $BFC$ are semicircles on diameters $AC,AB$ and $BC$ respectively.

Answer 1

We know:
Perimeter (circumference of a circle) $=2\pi r$
Perimeter of a semi-circle arc $=\pi r$
Now,
For the arc $ADC$, diameter is $2.8+1.4=4.2cm$
radius is $\frac{4.2}{2}=2.1cm.$
since radius is half of the diameter
Thus, Perimeter of the arc $ADC=\pi r=2.1\pi cm$
Similar way, for the arc $AEB$, diameter is $2.8cm$
radius is $\frac{2.8}{2}=1.4cm.$
Thus, ​Perimeter of the arc $AEB=\pi r=1.4\pi cm$

For the arc $BFC$, radius is $0.7cm.$
Thus, Perimeter of the arc $BFC=\pi r=0.7\pi cm$
Thus, we have:
Perimeter of the shaded region $=2.1\pi +1.4\pi +0.7\pi$
$=4.2\pi cm$
$=4.2\times \frac{22}{7}$
$=0.6\times 22$
$=13.2cm$
Hence, the perimeter of the shaded region is $=13.2cm$