Answered

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

Sagot :

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]

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