Circle question involving area?

Question

Suppose you are given a square with an inscribed circle if the area of the square is 100 meters squared what is the area of the circle?

Answer 1

Hint

Diameter of the circle is also the length of a side of the square, $10$ units.

Answer 2

Note that area of a square is given by $s^2$ where $s$ is the length of one of its sides (whichever side it may be, it doesn't matter for they are all equal.

So if $s^2=100 \implies s=\sqrt{100}=10 \text{ meters}$. The side of your square is $ 10$ meters. A circle inscribed in it would look something like this

Now Note that in the diagram, Since $\bar{DC}=10\text{ meters} \implies \bar{XY}= \bar{DC}=10 \text{m}$.

So we now have that the diameter $XY$ of the circle at $O$ is $10\text{ meters}$.(I made a mistake while making the diagram, it should have been $10 \text{m}$ not $10 \text{cm}$, I hope this won't be much of a problem)
Figuring out the area of a circle with a given diameter is an elementary geometry problem. The area of the circle hence is $\pi\cdot\big(\frac12\cdot10\text{m}\big)^2=(25\pi)\;\text m^2$