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:
[tex]A=\frac{\theta}{360}\ast\pi r^2[/tex]Where:
radius, r = DE = 15 units
θ = 36
Substitute values into the formula:
[tex]\begin{gathered} A=\frac{36}{360}\ast\pi\ast15^2 \\ \\ A=\frac{1}{10}\ast\pi\ast225 \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} A=0.1\pi\ast225 \\ \\ A=70.69\text{ square units} \end{gathered}[/tex]Therefore, the area of the sector rounded to the nearest hundredth is 70.69 square units
ANSWER:
[tex]\begin{gathered} ^{} \\ \text{ 70.69 units}^2 \end{gathered}[/tex]