1.

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

Answer»

strong>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{<klux>3</klux>}*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.


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