Question

A sector of a circle has a central angle of $135°$.

Find the area of the sector if the radius of the circle is $6ft$ . (Round your answer to one decimal place.)

Answer 1

Finding the area of the sector:

Given,

The central angle $\theta =135°$

The radius of the circle $r=6ft$

We know that,

Area of sector$=\frac{\theta }{360°}\times \mathrm{\pi }\times {\left(\mathrm{radius}\right)}^2$

$$\begin{gathered} =\frac{135°}{360°}\times 3.14\times {\left(6\right)}^2 \\ =\frac{135°}{360°}\times 3.14\times 36 \\ =42.39 \\ \approx 42.4 \end{gathered}$$

Hence, the area of the sector is $42.4{\mathrm{ft}}^2$.