A triangle has sides with lengths: 6, 11, and 9. How do you find the area of the triangle using Heron's formula?

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A triangle has sides with lengths: 6, 11, and 9. How do you find the area of the triangle using Heron's formula?

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Answer 1 · 2016-01-05T00:37:52

$A=2sqrt182$

Explanation:

First, find the triangle's semiperimeter. The semiperimeter is one half the perimeter of the triangle, which can be represented for a triangle with sides $a,b,$ and $c$ as

$s=(a+b+c)/2$

Thus,

$s=(6+11+9)/2=13$

Now, use Heron's formula to determine the area of the triangle. Heron's formula uses only the side lengths of the triangle to find the triangle's area:

$A=sqrt(s(s-a)(s-b)(s-c))$

$A=sqrt(13(13-6)(13-11)(13-9))$

$A=sqrt(13xx7xx2xx4)$

$A=2sqrt182$

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A triangle has sides with lengths: 6, 11, and 9. How do you find the area of the triangle using Heron's formula?

1 Answer

Explanation:

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