Question

In triangle ABC AB is 3cm,BC is 4cm and AC is 5cm,then find the area of triangle ABC

Answer 1

${\blue{\underline{\underline{\sf{Given :}}}}}$

• AB = 3cm

• BC = 4cm

• AC = 5cm

${\blue{\underline{\underline{\sf{To\:Find :}}}}}$

• Area of triangle ABC = ?

${\blue{\underline{\underline{\sf{Solution :}}}}}$

Using the formulas,

$\star \: {\purple{\boxed{\frak{Area = \sqrt{ s( s - a )( s - b)( s - c)}}}}}$

⠀⠀⠀⠀

$\star \: {\purple{\boxed{\frak{Semi\: Perimeter = \dfrac{ a + b + c}{2}}}}}$

⠀⠀⠀⠀

$\sf: \implies\: {\bold{ SP=\dfrac{ 3 + 4 + 5}{2}}}$

⠀⠀⠀⠀

$\sf: \implies\: {\bold{ SP =\dfrac{ 12 }{2}}}$

⠀⠀⠀⠀

$\sf: \implies\: {\boxed{\frak{ SP = 6cm }}}$

Now,

$\sf: \implies\: {\bold{ Area = \sqrt{6 ( 6 - 3)( 6 - 4)( 6 - 5)}}}$

⠀⠀⠀⠀

$\sf: \implies\: {\bold{ Area = \sqrt{6\times 3\times 2\times 1}}}$

⠀⠀⠀⠀

$\sf: \implies\: {\bold{ Area = \sqrt{2\times 3 \times 3\times 2\times 1}}}$

⠀⠀⠀⠀

$\sf: \implies\: {\bold{ Area = 2 \times 3\times 1}}$

⠀⠀⠀⠀

$\sf: \implies\: {\boxed{\frak{Area = 6cm^2}}}$

⠀⠀⠀⠀

So the final answer is,

• Area of triangle ABC = 6cm²