Question

In circle E with mZDEF 36 and DE = 15 units find area of sector DEF. Round to the nearest hundredth. E F D

Answer 1

Given:

m∠DEF = 36

DE = 15 units

Let's find the area of the sector.

To find the area of the sector, apply the formula:

`A=(\theta)/(360)\ast\pi r^2`

Where:

radius, r = DE = 15 units

θ = 36

Substitute values into the formula:

`\begin{gathered} A=(36)/(360)\ast\pi\ast15^2 \\ \\ A=(1)/(10)\ast\pi\ast225 \end{gathered}`

Solving further:

`\begin{gathered} A=0.1\pi\ast225 \\ \\ A=70.69\text{ square units} \end{gathered}`

Therefore, the area of the sector rounded to the nearest hundredth is 70.69 square units

ANSWER:

`\begin{gathered} ^{} \\ \text{ 70.69 units}^2 \end{gathered}`