Question

Find area of semicircle whose circumference is 55cm​

Answer 1

Answer:

circunfrence of a semicircle=pie r

22/7×x=55

x=55×7/22

x=35/2

x=17.5

area=22/7×17.5×17.5

=962.5

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Answer 2

Answer :-

The area of semi-circle is 481.25cm².

Step-by-step explanation :-

Concept :-

First we need to find out the radius, we can get the radius of semi-circle by circumference, as to find we need the radius of semi-circle.

To Find,

• The area of semi-circle

Solution,

Given that,

• Circumference of semi-circle = 55cm

As we know that,

$\dag \: \: \underline{\boxed{ \red{\sf{Circumference \: of \: semi-circle = \pi \: r}}}}$

Therefore, the radius is,

$\sf{\mapsto \: \pi \: r = 55cm} \\ \\ \\ \sf{\mapsto \: r = 55 \times \pi} \\ \\ \\ \sf{\mapsto \: r = 55 \times \dfrac{7}{22}} \\ \\ \\ \sf{\mapsto \: r = \cancel{55} \times \dfrac{7}{ \cancel{22}}} \\ \\ \\ \sf{\mapsto \: r = 5 \times \dfrac{7}{2}} \\ \\ \\ \sf{\mapsto \: r = \dfrac{5 \times 7}{2}} \\ \\ \\ \sf{\mapsto \: r = \dfrac{35}{2}} \\ \\ \\ \sf{ \underline{\therefore \: The \: radius \: of \: semi-circle \: is \: \dfrac{35}{7}}}$

Now, the area of semi-circle is,

As we know that,

$\dag \: \: \underline{\boxed{\sf{ \red{Area \: of \: semi-circle = \dfrac{1}{2} \times \pi \: {r}^{2}}}}}$

Therefore,

$\sf{ \mapsto \: \dfrac{1}{2} \times \dfrac{22}{7} \times {\bigg( \dfrac{35}{7} \bigg)^{2}}} \\ \\ \\ \sf{ \mapsto \: \dfrac{1}{2} \times \dfrac{22}{7} \times\dfrac{35}{2}} \: \times \: \dfrac{35}{2} \\ \\ \\ \sf{ \mapsto \: \dfrac{1}{2} \times \dfrac{ \cancel{22}}{ \cancel{7}} \times\dfrac{ \cancel{35}}{2}} \: \times \: \dfrac{35}{ \cancel{2}} \\ \\ \\ \sf{ \mapsto \: \dfrac{11 \times 5 \times 35}{2 \times 2}} \\ \\ \\ \sf{ \mapsto \: \dfrac{1925}{4}} \\ \\ \\ \sf{ \mapsto \: \cancel{ \dfrac{1925}{4}}} \\ \\ \\ \mapsto \: \frak{ \pink{481.25 {cm}^{2}}} \: \: \: \bigstar$

The area of semi-circle is 481.25cm².