Question

A 10 inch square is inacribed in circle find the aresa of circle

Answer 1

Hey, I have attached the solution to your question. Hope it helps you. :-)

The answer is 157.14 inch² ....
The value of π which I have taken is 22/7 . You can also solve it by taking the value of π = 3.14 ...

Thanks !

Answer 2

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Construction:Join Ac

In ∆ABC

By Pythagoras theorem:

$\bold{\boxed{ {AC}^{2} = {AB}^{2} + {BC}^{2}}}$

$= > {AC}^{2} = {10}^{2} + {10}^{2}$

$= > {AC}^{2} = 100 + 100$

$= > {AC}^{2} = 200$

$= > AC = 10 \sqrt{2}$

Now,AC is the diameter of the cirlce

It's radius =10√2/2=5√2inch

$\bold{\boxed{ = > Area \: of \: circle = \pi {r}^{2}}}$

$= > \frac{22}{7} \times {(5 \sqrt{2}) }^{2}$

$= > \frac{22}{7} \times 25 \times 2$

$= > \frac{22 \times 50}{7} = \frac{1100}{7} = 157.14$

$= > 157.14 {inch}^{2}$

$∴Area \: of \: circle \: is \: 157.14 {inch}^{2}$

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