# The perimeter of a sector of a circle of radius 5.6 cm is 27.2 cm.

Question:

The perimeter of a sector of a circle of radius 5.6 cm is 27.2 cm. Find the area of the sector.

Solution:

Let O be the centre of the circle with radius 5.6 cm and OACB be its sector with perimeter 27.2 cm.
Thus, we have:

$O A+O B+\operatorname{arc} A B=27.2$

$\Rightarrow 5.6+5.6+\operatorname{arc} A B=27.2$

$\Rightarrow \operatorname{arc} A B=16 \mathrm{~cm}$

Now,

Area of the sector $O A C B O=\left(\frac{1}{2} \times\right.$ Radius $\left.\times l\right)$ square units

$=\left(\frac{1}{2} 5.6 \times 16\right) \mathrm{cm}^{2}$

$=44.8 \mathrm{~cm}^{2}$
The text passage contains a mathematical question about finding the area of a sector of a circle, and it provides a detailed solution to the problem.
single_question_with_answer
Given a text passage, determine:
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    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
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- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# The perimeter of a sector of a circle of radius 5.6 cm is 27.2 cm.

Question:

The perimeter of a sector of a circle of radius 5.6 cm is 27.2 cm. Find the area of the sector.

Solution:

Let O be the centre of the circle with radius 5.6 cm and OACB be its sector with perimeter 27.2 cm.
Thus, we have:

$O A+O B+\operatorname{arc} A B=27.2$

$\Rightarrow 5.6+5.6+\operatorname{arc} A B=27.2$

$\Rightarrow \operatorname{arc} A B=16 \mathrm{~cm}$

Now,

Area of the sector $O A C B O=\left(\frac{1}{2} \times\right.$ Radius $\left.\times l\right)$ square units

$=\left(\frac{1}{2} 5.6 \times 16\right) \mathrm{cm}^{2}$

$=44.8 \mathrm{~cm}^{2}$
user
The text passage contains a mathematical question about finding the area of a sector of a circle, and it provides a detailed solution to the problem.

TYPE: SINGLE_QUESTION_WITH_ANSWER