find the area of the triangle with sides 5, 6 and root 13 units

Dear Student,

To find the area of a triangle when the three sides are given, we use the Heron's formula.

Let the triangle be ABC and a = 5, b=6 and c = 13

Now, Heron's formula is given as:

Area = S(S-a)(S-b)(S-c)where S= a+b+c2, and  a,b,c are the sides of the triangle. 
So, S=5+6+132So,Area = 5+6+132(5+6+132-5)(5+6+132-6)(5+6+132-13)= 11+132(11+13-102)(11+13-122)(11+13-2132)=11+132(1+132)(-1+132)(11-132)=11+132(1+132)(-11+13+1113-134)=11+132(1+132)(-24+12134)=11+132(-24+1213-2413+1568)=11+132(132-12138)=1452-13213+13213-15616=129616=81=9

Thus, the correct answer is 9 units.

Hope it helps.


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