How do you use Heron's formula to determine the area of a triangle with sides of that are 5, 6, and 3 units in length?

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Answer 1 · 2016-01-25T05:28:55

$Area=2sqrt14$ square units

$Area=7.48331$ square units

The Heron's formula to determine the area of a triangle is:

$Area=sqrt(s(s-a)(s-b)(s-c))$

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

$s$ is one-half of the perimeter of the triangle.

To compute for the area of the triangle using the Heron's Formula, the $s$ should be computed first.

Since the given sides are $a=5$ , $b=6$ , and $c=3$ .

$s=1/2*(5+6+3)=7$

$s=7$

Compute the Area after computing s:

$Area=sqrt(7(7-5)(7-6)(7-3))$

$Area=sqrt(7(2)(1)(4))$

$Area=2sqrt(14)$

$Area=7.48331$ square units

Have a nice day!!! from the Philippines ....

Answer 2 · 2018-06-15T23:50:23

There's always a better alternative than Heron's Formula. Area $S$ satisfies

$16S^2 = (a+b+c)(-a+b+c)(a-b+c)(a+b-c)=(5+6+3)(-5+6+3)(5-6+3)(5+6-3)=14(4)(2)(8)$ or

$S=2 sqrt{14}.$