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.

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We can use this formula .

#p = (a + b + c) /2# where p is the half of perimeter of triangle.

Thus # S = sqrt{p(p-a)(p-b)(p-c)} # 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 = (3 + 4 + 5) /2 = 6#

Than the formula for area :

# S = sqrt{6 ( 6 - 3) (6 - 4 ) (6 - 5)} = #

# sqrt{ 6 *3 *2*1 } = sqrt36 = 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=(a*b)/2 = (3 * 4)/ 2 = 6 #

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

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