Finding the area of the shaded region on a circle.

Question

So I need help finding the area of the shaded A region. I was going to do pi*(r^2)*(45/360) - (the area of the smaller triangle). I just dont know how to get the angle or the lengths of it. Is there an easier way to solve this problem?

Answer 1

The two lines $y=-\frac{1}{4}x+3$ and $y=x$ meet at $(12/5,12/5)$. So the little triangle has base $3$ and height $12/5$. Here the base is the vertical line segment joining the origin to the point $(0,3)$.

Answer 2

HINT:

$$S_{A_3}=\dfrac{1}{8}S_{C_9}-S_{\bigtriangleup }=\dfrac{\pi r^2}{8}-\dfrac{1}{2}\cdot 3\cdot \dfrac{12}{5}$$