How do you use Heron's formula to determine the area of a triangle with sides of that are 28, 29, and 32 units in length?

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Answer 1 · 2016-05-02T09:27:27

Area of triangle is $377.175$ units

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

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

Here the three sides are $28$ , $29$ and $32$ and hence

$s=1/2(28+29+32)=89/2$

Hence area of triangle is

$sqrt(89/2xx(89/2-28)xx(89/2-29)xx(89/2-32)$

or = $sqrt(89/2xx33/2xx31/2xx25/2)$

or $5/4sqrt(89xx33xx31)=5/4sqrt91047=5/4xx301.74=377.175$ units.