Question

Find the area of a triangle whose sides are measures 12cm 6cm 15cm

Answer 1

$\Large \underline{ \textbf{Given}}$

To Find area of a triangle whose sides measures 12cm , 6cm and 15cm

$\Large \underline{ \textbf{Solution}}$

Let -

First Side ( a ) = 12cm

Second Side ( b ) = 6cm

Third Side ( c ) = 15cm

Now to find area of a triangle we have a formula known as $\underline{\textbf{Heron's Formula }}$

by this formula we have --

$\boxed{\mathbf{Area \: of \: Triangle \: = \: \sqrt{s(s - a)(s - b)(s - c)}}}$

Where

$\mathbf{S\: =\: Semi-Perimeter\: = \:\dfrac{a + b + c}{2}}$

$\underline{\textbf{Step - 1 ) Form an equation with help of the above formula }}$

Now by Putting Values of a = 12cm , b = 6cm , c = 15cm in this Formula We have $\implies$

$\mathbf{Area \: of \: triangle \: = \sqrt{s(s - 12)(s - 6)(s - 15)}}$

Now we know that

$\sf{S\: = \: \dfrac{a+b+c}{2}}$

That is

$\sf{S\: = \: \dfrac{12cm + 6cm + 15cm}{2}\:=\:16.5 cm}$

Now Putting value of ' S ' in the obtained formula we have $\implies$

$\mathbf{Area \: of \: triangle \: = \sqrt{16.5(16.5 - 12)(16.5 - 6)(16.5 - 15)}}$

$\underline{\textbf{Step-2 ) Solve the obtained equation}}$

$\mathbf{Area \: of \: triangle \: = \sqrt{16.5(16.5 - 12)(16.5 - 6)(16.5 - 15)}}$

$\mathbf{\implies \:\sqrt{16.5(4.5)(10.5)(1.5)}}$

$\mathbf{\implies \:\sqrt{16.5(70.875)}}$

$\mathbf{\implies \:\sqrt{16.5(70.875)}}$

$\mathbf{\implies \:\sqrt{1,169.4375\:cm^4}}$

That is

$\mathbf{Area \: of \: triangle\: = \: 34.12\:cm^2 (Approx)}$

$\underline{\bf{Hence\: The\: Required \:Answer \:Is\: \implies}}$

$\boxed{\boxed{\mathbf{Area \: = \:34.12 \:cm^2}}}$

Answer 2

ANSWER:-

Given:

A triangle whose sides are measures 12cm, 6cm & 15cm.

To find:

Find the area of a triangle.

Solution:

Using the Heron's Formula

⏺️A= 12cm

⏺️B= 6cm

⏺️C= 15cm

$s = \frac{A + B + C}{2} \\ \\ = > \frac{12 + 6 + 15}{2} \\ \\ = > \frac{33}{2} \\ \\ = > 16.5cm$

Therefore,

Semi- perimeter= 16.5cm

Now,

We know that area of triangle is;

$A(\triangle\:ABC) = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ = > \sqrt{16.5(16.5 - 12)(16.5 - 6)(16.5 - 15)} \\ \\ = > \sqrt{16.5(4.5)(10.5)(1.5)} \\ \\ = > \sqrt{1169.43} \\ \\ = > 34.19 {cm}^{2}$

Hence,

The area of triangle is 34.19cm².

Hope it helps ☺️