text: ×
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  # Area of Triangles
  
  You know that Area = base x height / 2, but what other ways are there to find the area of a triangle? Brace yourself for some potent formulae.
  
  # Area of Triangles: Level 3 Challenges
  
  Triangle $$ABC$$ has coodinates $$A= (-4, 0)$$, $$B= (4 , 0)$$, and $$C= (0 , 3)$$.
  
  Let $$P$$ be the point in the first quadrant such that $$\triangle ABP$$ has half the area of $$\triangle ABC$$ but both triangles have the same perimeter.
  
  What is the length of $$CP$$? If your solution is in a form of $$\sqrt{d}$$, submit $$d$$ as the answer.
  
  Let $$ABCD$$ be a square of side length 12.
  
  • $$E$$ is the midpoint of $$CB$$,
  • $$FC = \frac{1}{3} DC$$,
  • $$GD = \frac{1}{4} DA$$,
  • $$AH = \frac{1}{3} AE$$,
  • $$J$$ is the midpoint of $$FE$$.
  
  What is the area of the purple triangle?
  
  Which of the following triangles has a larger area:
  
  • triangle A with side lengths $$13, 13, 10$$, or
  • triangle B with side lengths $$13, 13, 24\, ?$$
  
  In the figure above triangle $$ABC$$ with side-lengths $$AC=14$$, $$AB=13$$ and $$BC=15.$$ The incircle is drawn, which is tangential to all three sides. If the green shaded region is equal to $$A$$, find $$\left\lfloor A\right\rfloor$$.
  
  What is the largest possible area of an isosceles triangle with two sides of length 2?
  
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explanation: The document contains a series of math problems related to the area of triangles. Each problem is a distinct question, and there are no provided answers.
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: ×
  Back to all chapters
  
  # Area of Triangles
  
  You know that Area = base x height / 2, but what other ways are there to find the area of a triangle? Brace yourself for some potent formulae.
  
  # Area of Triangles: Level 3 Challenges
  
  Triangle $$ABC$$ has coodinates $$A= (-4, 0)$$, $$B= (4 , 0)$$, and $$C= (0 , 3)$$.
  
  Let $$P$$ be the point in the first quadrant such that $$\triangle ABP$$ has half the area of $$\triangle ABC$$ but both triangles have the same perimeter.
  
  What is the length of $$CP$$? If your solution is in a form of $$\sqrt{d}$$, submit $$d$$ as the answer.
  
  Let $$ABCD$$ be a square of side length 12.
  
  • $$E$$ is the midpoint of $$CB$$,
  • $$FC = \frac{1}{3} DC$$,
  • $$GD = \frac{1}{4} DA$$,
  • $$AH = \frac{1}{3} AE$$,
  • $$J$$ is the midpoint of $$FE$$.
  
  What is the area of the purple triangle?
  
  Which of the following triangles has a larger area:
  
  • triangle A with side lengths $$13, 13, 10$$, or
  • triangle B with side lengths $$13, 13, 24\, ?$$
  
  In the figure above triangle $$ABC$$ with side-lengths $$AC=14$$, $$AB=13$$ and $$BC=15.$$ The incircle is drawn, which is tangential to all three sides. If the green shaded region is equal to $$A$$, find $$\left\lfloor A\right\rfloor$$.
  
  What is the largest possible area of an isosceles triangle with two sides of length 2?
  
  ×
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a series of math problems related to the area of triangles. Each problem is a distinct question, and there are no provided answers.
  
  Label: multiple-question