Question

if the perimeter of a semi-circular park is 72 m, find its area and area​

Answer 1

Answer:-

The required area of park is 308m².

Full Solution:-

Given:-

Perimeter of semi-circular park=72m

$\rule{300}{2}$

To find:

Area of semi-circular park

$\rule{300}{2}$

Step-by-step explanation:-

The perimeter of semi-circular park includes:

→ Diameter of park+ ½ length of its circumference

→ 2r+½ (2πr)

→ 2r+πr

So perimeter of semi-circular park=2r+πr

$\sf\to72m=r(2+\pi)$

$\sf\to 72m=r\bigg[2+\dfrac{22}{7}\bigg]$

$\sf\to 72m=r\bigg[\dfrac{14+22}{7}\bigg]$

$\sf\to 72m=r\bigg[\dfrac{36}{7}\bigg]$

$\sf\to 72m\times\dfrac{7}{36}=r$

$\sf\to 2\times7m=r$

$\underline{\boxed{\sf\Longrightarrow 14 m=r}}$

The radius of semi-circular park is 14m.

$\rule{300}{2}$

Now we have formula for area:

★ Area of circle=2πr

Area of semi-circle=½(πr²)

Now put value of radius

$\sf\: Area \:of \;semi-circle=\dfrac{1}{2} \times\dfrac{22}{7} \times14\times14$

$\sf\: Area \:of \;semi-circle=30m^{2}$

$\rule{300}{2}$