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Geometry Level 2

What is the area of a triangle with sides 20, 13 and 11?


The answer is 66.

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Denton Young by Denton Young , 47, USA

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3 solutions

Denton Young
Apr 11, 2017

Relevant wiki: Area of Triangles - Heron's Formula

The semi-perimeter is ( 20 + 13 + 11 ) / 2 (20 + 13 + 11)/2 = 22 22

So by Hero's formula, A = ( 22 ) ( 22 − 20 ) ( 22 − 13 ) ( 22 − 11 ) A = \sqrt{(22)(22-20)(22-13)(22-11)} = 2 2 2 × 3 2 \sqrt{22^2 \times 3^2} = 22 × 3 22 \times 3 = 66 66

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Ajit Athle
Sep 11, 2018

Interestingly, Area (20-13-11) = Area (20-16-12) - Area (13-12-5). Then A = 11x12/2 = 66

1 Helpful 0 Interesting 0 Brilliant 0 Confused

It is easy - just use the Herons formula

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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