Question

61. What is the area of a semicircle having perimeter 90 cm?
(1) 481.25 cm
(2) 962.5 cm
(3) 1995 cm
(4) 240.63 cm​

Answer 1

Given:-

• Perimeter of Semicircle = 90 cm

To Find:-

• Area of a semicircle

Formula Used:-

• ${\boxed{\bf{Perimeter\:of\:Semi-Circle=\dfrac{1}{2}\times 2\pi r + 2r}}}$

• ${\boxed{\bf{Area\:of\:Semi-Circle=\dfrac{1}{2}\times \pi r^2}}}$

Solution:-

Firstly,

$\sf :\implies\:Perimeter=\dfrac{1}{2}\times 2\pi r + 2r$

$\sf :\implies\:90=r(\pi +2)$

$\sf :\implies\:90=r(\dfrac{22}{7}+2)$

$\sf :\implies\:90=r\times \dfrac{22+14}{7}$

$\sf :\implies\:90=r\times \dfrac{36}{7}$

$\sf :\implies\:r= \dfrac{90\times7}{36}$

$\sf :\implies\:r= \dfrac{10\times7}{4}$

$\sf :\implies\:r= \dfrac{35}{2}\:cm$

Now,

$\sf :\implies\:Area\:of\:Semi-Circle=\dfrac{1}{2}\times \pi r^2$

$\sf :\implies\:Area=\dfrac{1}{2}\times \dfrac{22}{7}\times \dfrac{35}{2}\times \dfrac{35}{2}$

$\sf :\implies\:Area=11\times \dfrac{5}{2}\times \dfrac{35}{2}$

$\sf :\implies\:Area=\dfrac{11\times5\times35}{4}$

$\sf :\implies\:Area=\dfrac{1,925}{4}\:cm^2$

$\sf :\implies\:Area=481.25\:cm^2$

Hence, The Area of Semi Circle is 481.25cm².

{Option 1 is correct}

━━━━━━━━━━━━━━━━━━