# 12 - Circular sector inscribed in a square

**Problem 12**

A circular sector of radius 10 cm is inscribed in a square of sides 10 cm such that the center of the circle is at the midpoint of one side of the square. Find the area of the sector in cm^{2}.

**Solution 12**

$\cos \alpha = \dfrac{5}{10}$

$\alpha = 60^\circ$

$\theta = 180^\circ - 2\alpha$

$\theta = 180^\circ - 2(60)$

$\theta = 60^\circ$

$\dfrac{A_\text{sector}}{\theta_\text{degree}} = \dfrac{\pi r^2}{360^\circ}$

$\dfrac{A_\text{sector}}{60^\circ} = \dfrac{\pi(10^2)}{360^\circ}$

$A_\text{sector} = 52.36 ~ \text{cm}^2$ *answer*

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