Area of triangle

Geometry Level 1

What is the area of a triangle with sides 17, 26, 25?

174 204 184 194

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Bob Yang by Bob Yang , 23, USA

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2 solutions

We can construct this triangle by "backing" right triangles of side lengths ( 7 , 24 , 25 ) (7,24,25) and ( 10 , 24 , 26 ) , (10,24,26), respectively, onto one another such that they share a mutual (vertical) side of length 24. 24. The triangle so constructed then has a base of length 7 + 10 = 17 7 + 10 = 17 and height 24 , 24, giving us an area of

1 2 × 17 × 24 = 204 . \dfrac{1}{2} \times 17 \times 24 = \boxed{204}.

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Moderator note:

Very creative use of Pythagoras Triplets! Here's an upvote!

Denton Young
Aug 6, 2015

The semi-perimeter is 34, so by Heron's formula, A = ( 34 ) ( 34 − 17 ) ( 34 − 26 ) ( 34 − 25 ) = 204 A = \sqrt{(34)(34-17)(34-26)(34-25)} = 204

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Moderator note:

Yes. This is the standard approach to solve the area of a triangle with all 3 sides given.

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