How do you use Heron's formula to determine the area of a triangle with sides of that are 8, 3, and 10 units in length?

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Answer 1 · 2016-09-10T15:14:43

Area of triangle is $9.922$

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

$Delta=sqrt(s(s-a)(s-b)(s-c))$ , where $s=1/2(a+b+c)$

Here we have three sides of a triangle as $8$ , $3$ and $10$ .

Hence $s=1/2(8+3+10)=1/2xx21=21/2$

and $Delta=sqrt(21/2(21/2-8)(21/2-3)(21/2-10))$

= $sqrt(21/2xx5/2xx15/2xx1/2)$

= $1/4sqrt(3xx7xx5xx3xx5)$

= $15/4xxsqrt7$

= $15/4xx2.6458$

= $9.922$