Question

find the area of triangle ABC by heron formula given side 3,4,5.

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Answer 1

Given:

The measurements of the sides of the triangle ABC are:

• 3 cm,
• 4 cm, and
• 5 cm.

To Find:

The area of the triangle ABC using Heron's Formula.

Heron's Formula:

$\pink {\sf {Area = \sqrt{ s(s - a)(s - b)(s - c)}}}$

where, s stands for Semi Perimeter, a, b, c stands for the given sides.

Explanation:

Semi Perimeter = a + b + c / 2

Semi Perimeter = 3 + 4 + 5 / 2

Semi Perimeter = 12 / 2

Semi Perimeter = 6 cm

$\purple {\sf {Area = \sqrt{6(6 - 3)(6 - 4)(6 - 5)}}}$

$\red {\sf {Area = \sqrt{6(3)(2)(1)}}}$

$\green {\sf {Area = \sqrt{36}}}$

$\orange {\sf {Area = 6 \: {cm}^{2}}}$

Answer:

The area of the triangle ABC is $\huge \blue {\sf {6 \: {cm}^{2}.}}$