Question

Find the area of a triangle whose sides are
13 cm, 14 cm and 15 cm respectively.​

Answer 1

Step-by-step explanation:

area of triangle=1/2×base×height

=1/2×13×14

=13×7

=91 cm²

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Answer 2

Given:

• First side of the triangle = 13 cm
• Second side of the triangle = 14 cm
• Third side of the triangle = 15 cm

To find:

• Area of the triangle.

Solution:

When the sides of the triangle are known, we use the Heron's formula to find its area.

Heron's formula:

$\boxed {\mathfrak {\pink {A = \sqrt{s(s - a)(s - b)(s - c)}}}}$

Where,

A = area

s = half of the triangle's perimeter

a, b, c = sides of the triangle

First we will calculate the value of 's', that is half the perimeter of the triangle.

Perimeter:

We know that,

$\boxed {\mathfrak {\red {Perimeter\ of\ triangle = Sum\ of\ all\ sides}}}$

Perimeter = (13+14+15) cm

$\boxed {\bf {\orange {Perimeter = 42\ cm}}}$

Half perimeter = $\sf \dfrac {42}{2}$

Half perimeter = 21 cm

Using Heron's formula:

Substitute the values in the formula,

$\sf{a = \sqrt{21(21 - 13)(21- 14)(21 - 15)}}$

$\sf{a = \sqrt{21 \times 8 \times 7 \times 6}}$

$\sf{a = \sqrt{7056}}$

$\boxed {\bf {\blue {Area = 84\ cm^{2}}}}$

Area of triangle:

Area of the triangle is 84 cm².