Suppose I have the following sector form with radius $1$, with $60°$. I divide the sector form into three pieces with an equal degree $(20°)$ and connect four points in the picture and try to calculate the area.
How one can compute the area without calculus?
My first guess was using $A=\frac{1}{2}r^2θ$ and try to decompose the figures into triangles and small sector forms. But at some points I lost. Actually via equations of circle and computing intersection points and do integration I compute the area but I think that was too harsh.
Hint: The area of the unknown region is given as $$\text{Area}(\text{sector}\ CDE)-\text{Area}(\triangle EHD)+\text{Area}(\square FCHG)$$
Note that $\square FCHG$ is a trapezium. Coordinates of the point $H$ are $\displaystyle\left(\frac{\sin20°\cdot\cos40°}{\sin40°},\sin20°\right)$.