Question

The sides of a triangle are 52 CM 56 cm and 6 cm find the area of triangle with heron's formula

Answer 1

Given:

Side if the triangles are

• a = 52 cm
• b = 56 cm
• c = 6 cm

To find:

The area of the triangle by Heron's formula

Heron's Formula

$= \sqrt{S(S-a)(S-b)(S-c)}$ units sq.

Here,

'S' = half of perimeter i.e. (perimeter/2)

And 'a', 'b', and 'c' are the sides of the triangle.

Now,

Periemter of the triangle = sum of all three sides of a triangle

Perimeter = 52 + 56 +  6 = 114

Now,

S = Perimeter/2 = 114/2

S = 57

• The area of the triangle is

$= \sqrt{S(S-a)(S-b)(S-c)}$ units sq.

$= \sqrt{57(57-52)(57 - 56)(57-6)}$

$= \sqrt{57*(5) *(1) * (51)}$

$= \sqrt{\underline{3}*19*5*1*\underline{3}*17}$

$= 3\sqrt{19*5*17}$

$= 3*\sqrt{1615}$

= 3 * 40.18

= 120.54 cm sq. (Approx.)

Hence,

• The area of the triangle with given sides is 120.54 cm sq.