How do you use Heron's formula to determine the area of a triangle with sides of that are 15, 16, and 12 units in length?

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How do you use Heron's formula to determine the area of a triangle with sides of that are 15, 16, and 12 units in length?

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Answer 1 · 2016-04-11T05:08:57

Area of triangle is $107.32$ $107.32$ units.

Explanation:

If three sides of a triangle are $a$ $a$ , $b$ $b$ and $c$ $c$ , according to Heron's formula its area is given by

$\sqrt{s (s - a) (s - b) (s - c)}$ $sqrt(s(s-a)(s-b)(s-c))$ , where $s = \frac{1}{2} (a + b + c)$ $s=1/2(a+b+c)$ is semi perimeer of the triangle.

In the given triangle the three sides are $15$ $15$ , $16$ $16$ and $12$ $12$ and semi perimeter is $\frac{1}{2} \times (15 + 16 + 12) = \frac{1}{2} \times 43 = 21.5$ $1/2xx(15+16+12)=1/2xx43=21.5$ .

Hence area is given by

$\sqrt{22.5 (22.5 - 15) (22.5 - 16) (22.5 - 12)}$ $sqrt(22.5(22.5-15)(22.5-16)(22.5-12))$

or $\sqrt{22.5 \times 7.5 \times 6.5 \times 10.5} = \sqrt{11517.1875} = 107.32$ $sqrt(22.5xx7.5xx6.5xx10.5)=sqrt11517.1875=107.32$

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How do you use Heron's formula to determine the area of a triangle with sides of that are 15, 16, and 12 units in length?

1 Answer

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