Three circular arcs of radius $5$ units bound the region shown. Arcs AB and AD are quarter-circles, and arc BCD is a semicircle.
I tried to find the answer by calculating the total area of the circle if it was a full one,and then I subtracted the area of the two quarter circles:
$$
\pi 5^{2} – 1/4\pi 5^{2} – 1/4 \pi r 5^{2} = 39.25
$$
but the answer should be $50$, why doesn't this approach work
${\large ?}$.
Best Answer
To answer the question as to why it doesn't work: draw the entire circle. Your cuts are not actually removing the entirety of two quarter circles, but only a section thereof.