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JH

# Prove the formula $A = \frac{1}{2} r^2 \theta$ for the area of a sector of a circle with radius $r$ and central angle $\theta$. [Hint: Assume $0 < 0 < \frac{\pi}{2}$ and place the center of the circle at theorigin so it has the equation $x^2 + y^2 = r^2$.Then $A$ is the sum of the area of the triangle $POQ$ and the area of the region $PQR$ in the figure.]

## $$\frac{1}{2} r^{2} \theta$$

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