The length of a chain used as the boundary of a semicircular park is 108 m.
Question:

The length of a chain used as the boundary of a semicircular park is 108 m. Find the area of the park.

 

Solution:

Let the radius of the park be r.
Length of chain = Perimeter of the semicircular park
⇒ 108 = Length of the arc + Diameter

$\Rightarrow 108=\frac{1}{2} \times 2 \pi r+2 r$

$\Rightarrow 108=r\left(\frac{22}{7}+2\right)$

$\Rightarrow 108=\frac{36}{7} r$

$\Rightarrow r=21 \mathrm{~m}$

Now, Area of park $=\frac{1}{2} \pi r^{2}=\frac{1}{2} \times \frac{22}{7} \times(21)^{2}=693 \mathrm{~m}^{2}$

Hence, the area of the park is 693 m2 

 

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