Question

1. Find the area of a triangle whose sides are 12 cm, 6 cm and 15 cm.

Answer 1

$\huge{ \colorbox{pink} {\color{green}{answer}}}$

A≈34.2cm²

Answer 2

Given : Sides of triangle are 12 cm, 6 cm and 15 cm

To find : The area of triangle

Solution :

To solve this problem, we will use the concept of " Heron's formala ", according to which,

$\sf:\to Area\:of\:triangle = \sqrt{S(S-A)(S-B)(S-C)}$

Here,

• S = Semi Perimeter
• A = Side 1
• B = Side 2
• C = Side 3

From this, it's clear that firstly we have to find the semi perimeter of triangle inorder to further find the area.

Let's assume that,

• A = 12 cm
• B = 6 cm
• C = 15 cm

Semi perimeter of triangle is given by,

${ \leadsto \sf \: Semi \: perimeter = \dfrac{A + B + C}{2}}$

${ \leadsto \sf \: Semi \: perimeter = \dfrac{12 \: cm + 15 \: cm + 6 \: cm}{2}}$

${ \leadsto \sf \: Semi \: perimeter = \dfrac{33\: cm}{2}}$

$\boxed{ \purple{ \leadsto \sf \: Semi \: perimeter = 16.5 \: cm}}$

Now apply " Heron's formala " :-

$\sf:\implies Area\:of\:\triangle = \sqrt{S(S-A)(S-B)(S-C)}$

$\sf:\implies Area\:of\:\triangle = \sqrt{16.5\:cm(16.5\:cm-12\:cm)(16.5\;cm-6\:cm)(16.5\:cm-15\:cm)}$

$\sf:\implies Area\:of \: \triangle = \sqrt{16.5\:cm(4.5\:cm)(10.5\;cm)(1.5\:cm)}$

$\sf:\implies Area\:of \: \triangle = \sqrt{1169.43 \: cm ^{4} }$

$\boxed{ \red{\sf:\implies Area\:of \: \triangle = 34.19 \: cm ^{2} }}$

So the required area of triangle is 34.19 cm².