# How do you find the area of a triangle with 3 sides given?

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Oct 26, 2014

Has some way to find the area of triangle with 3 sides given .

1) Assume that we are given a, b, c like in picture and we want to find the area.

We can use this formula .

$p = \frac{a + b + c}{2}$ where p is the half of perimeter of triangle.

Thus $S = \sqrt{p \left(p - a\right) \left(p - b\right) \left(p - c\right)}$ is the area .

(This is also called the Heroni formula )

Example :
Find the area of triangle with a= 4 , b= 5 ,c=3 .

Use the half perimeter formula :

$p = \frac{3 + 4 + 5}{2} = 6$

Than the formula for area :

$S = \sqrt{6 \left(6 - 3\right) \left(6 - 4\right) \left(6 - 5\right)} =$

$\sqrt{6 \cdot 3 \cdot 2 \cdot 1} = \sqrt{36} = 6$

(We know that this is a right angle triangle based of information given By pithagora we can apply the formula

${a}^{2} + {b}^{2} = {c}^{2}$

${3}^{2} + {4}^{2} = {5}^{2}$

9+16 =25.

For this case we can aplly the formula of area

$S = \frac{a \cdot b}{2} = \frac{3 \cdot 4}{2} = 6$

But this a case only for right angle while the Herony formula is for all triangles
)

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