How do you use Heron's formula to determine the area of a triangle with sides of that are 9, 15, and 10 units in length?

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Answer 1 · 2016-01-11T08:02:21

$A r e a = 43.6348$ $Area=43.6348$ square units

Hero's formula for finding area of the triangle is given by
$A r e a = \sqrt{s (s - a) (s - b) (s - c)}$ $Area=sqrt(s(s-a)(s-b)(s-c))$

Where $s$ $s$ is the semi perimeter and is defined as
$s = \frac{a + b + c}{2}$ $s=(a+b+c)/2$

and $a, b, c$ $a, b, c$ are the lengths of the three sides of the triangle.

Here let $a = 9, b = 15$ $a=9, b=15$ and $c = 10$ $c=10$

$\Rightarrow s = \frac{9 + 15 + 10}{2} = \frac{34}{2} = 17$ $implies s=(9+15+10)/2=34/2=17$

$\Rightarrow s = 17$ $implies s=17$

$\Rightarrow s - a = 17 - 9 = 8, s - b = 2 and s - c = 7$ $implies s-a=17-9=8, s-b=2 and s-c=7$

$\Rightarrow s - a = 8, s - b = 2 and s - c = 7$ $implies s-a=8, s-b=2 and s-c=7$

$\Rightarrow A r e a = \sqrt{17 \cdot 8 \cdot 2 \cdot 7} = \sqrt{1904} = 43.6348$ $implies Area=sqrt(17*8*2*7)=sqrt1904=43.6348$ square units

$\Rightarrow A r e a = 43.6348$ $implies Area=43.6348$ square units