Question

Find the perimeter of a semicircular region with a straight side that is 8 yards long.

Answer 1

Step 1: Find the distance around the curved path

Given: Diameter (d) = $8$ yards

We know that

Radius (r) = $\frac{d}{2}$

$\Rightarrow$r = $\frac{8}{2}$

$\therefore$r = $4$ yards

We also know that,

Distance around curved path = $\frac{\mathrm{Circumference}\mathrm{of}\mathrm{circle}}{2}$

$\Rightarrow$Distance around curved path = $\frac{2\mathrm{\pi r}}{2}$

$\Rightarrow$Distance around curved path = $\mathrm{\pi r}$

$\Rightarrow$Distance around curved path = $3.14\times 4$

$\therefore$Distance around curved path = $12.56$ yards

Step 2: Find the perimeter of a given figure.

Perimeter of given figure = Distance around curved path + Diameter of semicircular region

$\Rightarrow$Perimeter of given figure = $12.56+8$

$\therefore$Perimeter of given figure = $20.56$

Hence the perimeter of given figure is $20.56$yards