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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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The text passage contains multiple distinct mathematical questions or problems, but no answers are provided within the text for these questions.
multiple_questions
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    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>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
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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?

×
user
The text passage contains multiple distinct mathematical questions or problems, but no answers are provided within the text for these questions.

TYPE: MULTIPLE_QUESTIONS