A triangle has sides with lengths: 14, 8, 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, 8, and 12. How do you find the area of the triangle using Heron's formula?

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Answer 1 · 2016-02-11T08:44:28

Area of triangle is $47.906$ $47.906$

Explanation:

Heron's formula for area of triangle having three sides as $a$ $a$ , $b$ $b$ and $c$ $c$ is given by

$\sqrt{s (s - a) (s - b) (s - c)}$ $sqrt(s(s-a)(s-b)(s-c)$ where $s = \frac{1}{2} (a + b + c)$ $s=1/2(a+b+c)$

Here three sides are 14, 8 and 12. Thus $s = \frac{1}{2} (14 + 8 + 12)$ $s=1/2(14+8+12)$ i.e. $s = 17$ $s=17$ . Hence $s - a = 3$ $s-a=3$ , $s - b = 9$ $s-b=9$ and $s = c = 5$ $s=c=5$ .

Hence area of triangle is $\sqrt{17 \cdot 3 \cdot 9 \cdot 5}$ $sqrt(17*3*9*5$ or $\sqrt{2295}$ $sqrt 2295$ or $47.906$ $47.906$ .

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A triangle has sides with lengths: 14, 8, and 12. How do you find the area of the triangle using Heron's formula?

1 Answer

Explanation:

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