Question

In circle C with mZBCD = 66 and BC = 15 units find area of sector BCD. Round to the nearest hundredth. с B D

Answer 1

The area of sector BCD is 129.53 square units

Explanation:

The first thing is to calculate the area of the circle completely. That area would be for 360 °, therefore by means of a proportion we can calculate the area for the BDC sector.

The area of circle is:

`\begin{gathered} A=\pi\cdot r^2 \\ \text{replacing} \\ A=3.14\cdot15^2 \\ A=706.5 \end{gathered}`

Now, we calculate the area of the BDC sector by means of the following portion

`(706.5)/(360)=(x)/(66)`

Solving for x:

`\begin{gathered} x=66\cdot(706.5)/(360) \\ x=129.525\cong129.53 \end{gathered}`