Question

What is the area of a semicircle having perimeter 90 cm?
1) 481.25 cm
(2) 962.5 cm
(3) 1925 cm
(4) 240.63 cm
plzz answer fast with explanation​

Answer 1

Step-by-step explanation:

perimeter of semicircle =2pi r

90 /2pi. = r

315/22. =r

area of smicircle. =pi r^2/2

=pi ×315/22 ×315/22/2

Answer 2

We know,

$\boxed{ \large{ \bf{Area \: \: of \: \: semicircle} = \frac{\pi {r}^{2} }{2}}}$

But,

$\tt{Perimeter \: \: of \: \: semicircle = \pi r } \\ \\ \frak{ \: \: \: \: \: \: \: \: \: \: = > \pi r = 90 \: cm} \\ \frak{\: \: \: \: \: \: \: \: \: \: = > \: \: \: r = \frac{90 \times 7}{22} = \frac{315}{11} \: cm}$

Hence,

$\large{\bf{Area \: \: of \: \: this \: \: semicircle}} \\ \\ \implies \frac{1}{ \cancel2} \times \frac{ \cancel{22}}{7} \times { \bigg( \frac{315}{11} \bigg)}^{ \large2} \\ \\ \implies \frac{ \cancel{11}}{7} \times \frac{99225}{11 \times \cancel{ 11}} \\ \\ \implies \frac{99225}{77} = \red {1288}. \red{63} \sf \: {cm}^{2}$