1 Answer

Jeremiah · Answer 1 · 2023-05-13T05:57:04+0000

Question 7.

Given:

BD = 18 cm

m∠BEC = 136 degrees.

Let's find the area of the shaded sector.

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

$\text{Area}=2((\theta)/(360)*\pi r^2)$

Where:

θ = 136 degrees

r is the radius

To find the radius, we have:

Diameter, BD = 18 cm

Radius = diameter/2 = 18cm/2 = 9 cm

Now, substitute values into the formula and solve for the area.

$\begin{gathered} \text{Area}=2((136)/(360)*\pi*9^2) \\ \\ \text{Area}=2((136)/(360)*\pi*81) \end{gathered}$

Solving further, we have:

$\begin{gathered} Area=2(0.378\pi*81) \\ \\ \text{Area}=2(96.13) \\ \\ \text{Area}=192.27cm^2 \end{gathered}$

Therefore, the area of the shaded sector is 192.27 square cm.

ANSWER:

192.27 cm²

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