text: # 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
  
  $=\left(\frac{1}{2} 5.6 \times 16\right) \mathrm{cm}^{2}$
  
  $=44.8 \mathrm{~cm}^{2}$
explanation: The document contains a math problem and its solution. The problem asks for the area of a sector of a circle given the radius and the perimeter of the sector. The solution is provided, showing the steps to find the area.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # 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
  
  $=\left(\frac{1}{2} 5.6 \times 16\right) \mathrm{cm}^{2}$
  
  $=44.8 \mathrm{~cm}^{2}$
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math problem and its solution. The problem asks for the area of a sector of a circle given the radius and the perimeter of the sector. The solution is provided, showing the steps to find the area.
  
  Label: question-and-answer