# A chord with a length of 1  runs from pi/4  to pi/2  radians on a circle. What is the area of the circle?

Oct 13, 2017

Area $=$ 5.363 $\textcolor{w h i t e}{a}$sq.units

#### Explanation:

Angle at the center $= \frac{\pi}{2} - \frac{\pi}{4} = \frac{\pi}{4}$
Base angle each $= \frac{\pi - \left(\frac{\pi}{4}\right)}{2} = \frac{3 \pi}{8}$
$r \cdot \cos \left(\frac{3 \pi}{8}\right) = \frac{1}{2}$
$r = \frac{\frac{1}{2}}{\cos} \left(\frac{3 \pi}{8}\right) = 1.3066$

Area of the circle$= \pi \cdot {r}^{2} = \left(\frac{22}{7}\right) \cdot {1.3066}^{2} = 5.363$