Question

find the area of the smaller sector. round to the nearest tenth.
area = ? \text{ ft}^2

Explanation:

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<reasoning>

Identify the given values

Using the Sector Area Formula knowledge point
\[

$$\begin{aligned} &r = 7.13\text{ ft}\\ &\theta = 50^\circ \end{aligned}$$

\]

Calculate the area of the smaller sector

Using the Sector Area Formula knowledge point
\[

$$\begin{aligned} &\text{Area} = \frac{\theta}{360^\circ} \cdot \pi r^2\\ &\text{Area} = \frac{50}{360} \cdot \pi \cdot (7.13)^2\\ &\text{Area} = \frac{5}{36} \cdot \pi \cdot 50.8369\\ &\text{Area} \approx 0.13889 \cdot 3.14159265 \cdot 50.8369\\ &\text{Area} \approx 22.182\text{ ft}^2 \end{aligned}$$

\]

Round to the nearest tenth

Using the Sector Area Formula knowledge point
\[
\text{Area} \approx 22.2\text{ ft}^2
\]
</reasoning>

<answer>
Find the area of the smaller sector. Round to the nearest tenth.

Area = <blank>22.2</blank> \(ft^2\)
</answer>

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]
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Answer:

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<reasoning>

Identify the given values

Using the Sector Area Formula knowledge point
\[

$$\begin{aligned} &r = 7.13\text{ ft}\\ &\theta = 50^\circ \end{aligned}$$

\]

Calculate the area of the smaller sector

Using the Sector Area Formula knowledge point
\[

$$\begin{aligned} &\text{Area} = \frac{\theta}{360^\circ} \cdot \pi r^2\\ &\text{Area} = \frac{50}{360} \cdot \pi \cdot (7.13)^2\\ &\text{Area} = \frac{5}{36} \cdot \pi \cdot 50.8369\\ &\text{Area} \approx 0.13889 \cdot 3.14159265 \cdot 50.8369\\ &\text{Area} \approx 22.182\text{ ft}^2 \end{aligned}$$

\]

Round to the nearest tenth

Using the Sector Area Formula knowledge point
\[
\text{Area} \approx 22.2\text{ ft}^2
\]
</reasoning>

<answer>
Find the area of the smaller sector. Round to the nearest tenth.

Area = <blank>22.2</blank> \(ft^2\)
</answer>

<post_analysis>
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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Geometry",
"Sector Area Formula"
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