Question

find the area of triangle whose side is 12 cm 12cm 18cm. By heron's formula​

Answer 1

Answer:

A=77.44cm

Step-by-step explanation:

A side=12

B Base=12

C Side=18

Answer 2

Given -

• Side A = 12cn

• Side B = 12 cm

• Side C = 18cm

To find -

• Area of the triangle.

Formula used -

• Heron's formula.

Solution -

In the question, we are given, with 3 sides of a triangle, and we need to find the area, for that we cannot use, 1/2 × base × altitude, formula, so those questions, who have, 3 sides given, of a triangle, we use heron's formula, in this question too, we are going to use the Same, first we will find the semi-perimeter, then, we will apply,the heron's formula, let's do it!

According to the question -

Side A = 12 cm

Side B = 12 cm

Side C = 18 cm

First, we will, find th semi perimeter of the above sides.

$\sf \underline{semi - perimeter(s)} \: = \dfrac{a + b + c}{2}$

On substituting the values -

$\sf \: s = \dfrac{12 + 12 + 18}{2}$

$\sf \: s = \cancel \dfrac{42}{2}$

$\sf \: s = 21$

Now -

We are going to apply, heron's formula, and will find the area of the triangle.

$\sf \underline{heron's \: formula} = \sqrt{s(s - a)(s - b)(s - c)}$

Where -

S = Semi - perimeter

A = 1st side

B = 2nd side

C = 3rd side

On substituting the values -

$\sf \: \sqrt{21(21 - 12)(21 - 12)(21 - 18)}$

$\sf \: \sqrt{21 \times 9 \times 9 \times 3}$

$\sf \: \sqrt{5103}$

$\sf \longrightarrow \: 71.43 \: {cm}^{2}$

$\therefore$ The area of the triangle is 71.43cm²

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