How do you use Heron's formula to determine the area of a triangle with sides of that are 12, 6, and 10 units in length?

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Answer 1 · 2016-05-03T10:04:22

Area of triangle is $29.936$ $29.936$ .

According to Heron's formula, if the sides of a triangle are $a$ $a$ , $b$ $b$ and $c$ $c$ , then its area is given by

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

In the given triangle, sides are $12$ $12$ , $6$ $6$ and $10$ $10$ and hence

$s = \frac{1}{2} (12 + 6 + 10) = \frac{28}{2} = 14$ $s=1/2(12+6+10)=28/2=14$

Hence, area of triangle is

$\sqrt{14 \times (14 - 12) \times (14 - 6) \times (14 - 10)}$ $sqrt(14xx(14-12)xx(14-6)xx(14-10)$ or

$\sqrt{14 \times 2 \times 8 \times 4} = 8 \times \sqrt{14} = 8 \times 3.742 = 29.936$ $sqrt(14xx2xx8xx4)=8xxsqrt14=8xx3.742=29.936$