Question

The perimeter of a semicircular garden is 180m. Find the area of the garden.

Answer 1

$\mathtt{ \huge \purple{\underline{ \fbox{ \orange{ \: Solution : \: \: \: }}}}}$

Given ,

Perimeter of semicircle = 180 cm

We know that , the perimeter of Circle is given by

$\sf \large{ \fbox {Perimeter \: of \: semicircle = \pi ( r) }}$

$\sf \hookrightarrow 180 = \frac{22}{7} \times r \\ \\\sf \hookrightarrow r = \frac{1260}{22} \\ \\\sf \hookrightarrow r = 57.2 \: cm$

Now , the area of circle is given by

$\large \sf \fbox{Area \: of \: circle = \frac{\pi {(r)}^{2} }{2} }$

$\sf \hookrightarrow Area = \frac{ \cancel{22} \times {(57.2)}^{2} }{7 \times \cancel2} \\ \\ \sf \hookrightarrow Area = \frac{11 \times {(57.2)}^{2} }{7} \\ \\ \sf \hookrightarrow Area = \frac{11 \times 3271.84}{7} \\ \\ \sf \hookrightarrow Area = \frac{35990.24}{7} \\ \\ \sf \hookrightarrow Area = 5141.46 \: \: {cm}^{2}$

Hence , the area of circle is 5141.46 cm²