Question

A chord An divides a circle of radius 3 cm into two segments. If AB subtends a central angle of 45, find the area of the minor segment

Answer 1

check the picture below.

so the chord is the one in red there, making the segment, in green there, with a central angle of 45°, and the minor segment will be that green one.

$\bf \textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left[ \cfrac{\pi \theta }{180} - sin(\theta) \right]~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ ------\\ r=3\\ \theta =45 \end{cases} \\\\\\ A=\cfrac{3^2}{2}\left[ \cfrac{\pi(45) }{180} - sin(45^o) \right]\implies A=\cfrac{9}{2}\left[ \cfrac{\pi }{4}-\cfrac{\sqrt{2}}{2} \right] \\\\\\ A=\cfrac{9}{2}\left( \cfrac{\pi -2\sqrt{2}}{4} \right)\implies A\approx 0.3523112199491$