Question

Find the area of a triangle whose sides are 33cm,34cm and 65cm​

Answer 1

Answer:

Step-by-step explanation:

semi perimeter s=(a+b+c)/2

s=(33+34+65)/2= 132/2= 66

area of ▲ by heron's formula

area=square root[s(s-a)(s-b)(s-c)]

=square root[66×(66-33)(66-34)(66-65)]

=square root (66×33×32×1)

=square root (69696)

=264

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Answer 2

Given:

The sides of a triangle 33 cm, 34 cm, and 65 cm

To be found:

The area of the triangle

Now,

We can find the area of the triangle by Herons' formula.

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

[In which 'S' is the half of the perimeter and 'a', 'b' and 'c' are the sides of the triangle.]

Now,

Let a = 33, b = 34 and c = 65 sides of the triangle.

Now,

Perimeter of the triangle = 33+34+65 = 132

S = Periemter/2 = 132/2 = 66

Now,

BY using Herons' formula

Area  $= \sqrt{S(S- a)(S-b)(S-c)}$

         $= \sqrt{66(66- 33)(66-34)(66-65)}$

         $= \sqrt{66(33)(32)(1)}$

         $= \sqrt{11 \times 3 \times 2 \times 3 \times 11 \times 2^{5}}$

         $= \sqrt{\underline{2 \times 2} \times \underline{2\times 2}\times \underline{2\times 2} \times \underline{11 \times 11} \times \underline{3 \times 3}}$

         = 2 × 2 × 2 × 11 × 3

         = 8 × 33

         = 264 cm sq.

Hence,

The area of the triangle is 264 cm sq.