Question

find the area of a triangle whose sides are 40 cm ,24 cm ,32 cm by heron's formula.​

Answer 1

Answer:

384cm². It's a basic application of herons formula.

Answer 2

Here,

• a = 40cm.
• b = 24cm.
• c = 32cm.

$\large{ \mathtt{ \bold{S \: (semi \: perimeter) \: = \frac{a + b + c}{2} }}}$

$\implies \: S \: = \frac{40 + 24 + 32}{2}$

$\implies { \underline{ \bold{\: S \: = 48 \: cm.}}}$

$\bold{ \triangle \: Area \: of \: the \: triangle}$

$= \bold{\sqrt{s(s - a)(s - b)(s - c)} }$

$= \sqrt{48(48 - 40)(48 - 24)(48 - 32)}$

$= \sqrt{48 \times 8 \times 24 \times 16}$

$= \sqrt{147456}$

$= \large \boxed{\bold{138 \: {cm}^{2}} }$