I have been looking for a formula for these types of problems but I still haven't gotten an answer. The question you guys can use can be found here. All I need is the formula but if you want you can include the answer for the question. Also if you find the formula for a semicircle then please include that. Be sure to keep in mind that you need to include $2r$ in your formula.
Also if you are confused please tell me so I know whether I should elaborate.
$\endgroup$3 Answers
$\begingroup$The perimeter of a full circle is $2\pi r$. The perimeter of a quarter circle is therefore $P = \frac {2\pi r}4 + 2r$. The formula for the area of a full circle is $\pi r^2$. The area of a quarter circle is therefore $A= \frac {\pi r^2}4$.
So solve for $r$ in terms of $P$ and plug that equation into $A$.
I assume you can do that yourself.
$\endgroup$ 3 $\begingroup$First find the radius of the circle using the perimeter. For the quarter circle, the perimeter is made up of two lots of the radius plus a quarter of the circumference, so we have that $$2r + \frac{\pi}{2} r = P$$ giving that $$r = \frac{2P}{4 + \pi}$$ Now that you have the radius, you can use the area of a quarter circle formula to get the answer.
$\endgroup$ 3 $\begingroup$Hint -
$\frac14 \times 2\pi r + 2r = 5.355$
Find value of r.
Then put it in.
Area = $\frac14 \times \pi r^2$
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