Question

the sides of a triangle are 5 cm 12 cm and 13 cm find its area

Answer 1

You can find are of any triangle by HERON'S fromula if all its sides are known.
Here Sides are - 5 cm, 12 cm and 13 cm.
So, s = (a+b+c+)/2 where a,b, and c are sides of triangle
s = (5+12+13)/2 = 30/2 = 15
Area = \sqrt{s(s-a)(s-b)(s-c)}s(s−a)(s−b)(s−c)​ 
Area = \sqrt{15(15-5)(15-12)(15-13)} = \sqrt{15(10)(3)(2)} = \sqrt{(150)(6)} = \sqrt{900}15(15−5)(15−12)(15−13)​=15(10)(3)(2)​=(150)(6)​=900​
So, Area = 30 cm^{2}cm2 

And the smallest height will be on the largest base. So here the largest side is 13 cm.
So by area formula we have
Area = 1/2 *base * height
But area = 30 cm^{2}cm2 
so, 30 = 1/2 * 13 *height
height = 60/13 = 4.615 cm

Answer 2

Hi

Here is ur answer !!!!!!!!!

Answer:

Area = 30 cm²

Step-by-step explanation:

By applying Heron's formula,

S = (a + b + c )/ 2

  = ( 5 + 12 + 13 ) /2

S = 30 / 2

S = 15

Area =  √(S(s-a)  (s-b)  (s-c))

        = √ 15 ( 15 - 5 ) ( 15 - 12 ) ( 15 - 13)

        = √15 * 10* 3* 2

        = √900

Area = 30 cm²

Hope it helps U