Question

follow the steps to find the area of the shaded region.

last, subtract the triangle area from the sector area to find the area of the shaded region.

sector area = \\(78.6794\text{ cm}^2\\)

triangle area = \\(70.4956\text{ cm}^2\\)

area of the shaded region = \\(?\text{ cm}^2\\)

round to four decimal places.

Explanation:

<pre_analysis>
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"current_concepts": [
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"Area of Circular Segment"
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}
</pre_analysis>

<reasoning>

Identify the given values

\[

$$\begin{aligned} &\text{Sector Area} = 78.6794\text{ cm}^2\\ &\text{Triangle Area} = 70.4956\text{ cm}^2 \end{aligned}$$

\]

Subtract the triangle area from the sector area

\[

$$\begin{aligned} \text{Area of the Shaded Region} &= \text{Sector Area} - \text{Triangle Area}\\ &= 78.6794 - 70.4956\\ &= 8.1838\text{ cm}^2 \end{aligned}$$

\]
</reasoning>

<answer>
Follow the steps to find the area of the shaded region.

Last, subtract the triangle area from the sector area to find the area of the shaded region.

Sector Area = \(78.6794\text{ cm}^2\)

Triangle Area = \(70.4956\text{ cm}^2\)

Area of the Shaded Region = <blank>8.1838</blank> \(\text{cm}^2\)

Round to four decimal places.
</answer>

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"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Geometry",
"Area of Circular Segment"
]
}
</post_analysis>

Answer:

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"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [],
"new_concepts": [
"Area of Circular Segment"
],
"current_concepts": [
"Sector Area Formula",
"Triangle Area Formula",
"Area of Circular Segment"
]
}
</pre_analysis>

<reasoning>

Identify the given values

\[

$$\begin{aligned} &\text{Sector Area} = 78.6794\text{ cm}^2\\ &\text{Triangle Area} = 70.4956\text{ cm}^2 \end{aligned}$$

\]

Subtract the triangle area from the sector area

\[

$$\begin{aligned} \text{Area of the Shaded Region} &= \text{Sector Area} - \text{Triangle Area}\\ &= 78.6794 - 70.4956\\ &= 8.1838\text{ cm}^2 \end{aligned}$$

\]
</reasoning>

<answer>
Follow the steps to find the area of the shaded region.

Last, subtract the triangle area from the sector area to find the area of the shaded region.

Sector Area = \(78.6794\text{ cm}^2\)

Triangle Area = \(70.4956\text{ cm}^2\)

Area of the Shaded Region = <blank>8.1838</blank> \(\text{cm}^2\)

Round to four decimal places.
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Geometry",
"Area of Circular Segment"
]
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