Competition problem — Geometry — Maths Olympiad Prep

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Geometry Difficulty 3.4 AMC 10/12 Find the answer United States

Problem:
A triangle has sides of length $9$ , $40$ , and $41$ . What is its area?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Solution:
Observe that $9^{2} + 40^{2} = 41^{2}$ , so this triangle is right and therefore has area $\frac{1}{2} \cdot 9 \cdot 40 = 180$ .

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