A triangle has sides with lengths: 14, 9, and 12. How do you find the area of the triangle using Heron's formula?

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A triangle has sides with lengths: 14, 9, and 12. How do you find the area of the triangle using Heron's formula?

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Answer 1 · 2016-01-07T06:15:45

The area of the triangle is 53.5 square units.

Explanation:

Heron's formula is $A=sqrt(s(s-a)(s-b)(s-c))$ , where $A$ is area, $a, b,$ and $c$ are the sides of the triangle, and $s$ is the semiperimeter, which is half the perimeter.

The formula for the semiperimeter is $s=(a+b+c)/2$ .

Let side $a=14$ , side $b=9$ , and side $c=12$ .

Calculate the semiperimeter.

$s=(14+9+12)/2$

$s=35/2=17.5$

Calculate the area of the triangle.

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

$A=sqrt((17.5)(17.5-14)(17.5-9)(17.5-12))$

$A=53.5$ square units

Source: https://www.mathsisfun.com/geometry/herons-formula.html

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A triangle has sides with lengths: 14, 9, and 12. How do you find the area of the triangle using Heron's formula?

1 Answer

Explanation:

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