Question

If the perimeter of a semi circular park in 72m find its area and radius

Answer 1

$\large\sf{\underline{\underline{Given \ :}}}$

Perimeter of semi-circular park = 72 m

$\large\sf{\underline{\underline{Solution \ :}}}$

Perimeter of semi-circular park = Circumference of semi-circular park + Diameter of park

Also, Perimeter of semi-circular park = 72 m ( Given )

$\therefore$

Circumference of semi-circular park + Diameter of park = 72 m

πr + d = 72 m

Here, r = radius, d = diameter

${\boxed{\tt{Diameter, \ d = 2r}}}$

πr + 2r = 72

r ( π + 2 ) = 72

Taking π = 22 / 7

$\sf{r ( {\dfrac{22}{7}} + 2 ) = 72}$

$\sf{r ( {\dfrac{22 + 14}{7}} ) = 72}$

$\sf{r * {\dfrac{36}{7}} = 72}$

Transposing

$\sf{r = {\dfrac{72*7}{36}}}$

r = 14

Now,

Area of semi-circular park = $\sf{ {\dfrac{ \pi r^2}{2}}}$

Taking π = 22 / 7

= $\sf{ {\dfrac{ {\dfrac{22}{7}} . (14)^2}{2}} }$

= $\sf{ {\dfrac{22 . 14 . 14}{7 . 2}}}$

= 308 m²

Hence,

Radius of semi-circular park = 14 m

Area of semi-circular park = 308 m²