Question

find area of triangle by heron's formula ​

Answer 1

Using heron's formula,

$\sf{S = \frac{28 + 15 + 41}{2} } = \cancel\frac{^{42} \: 84}{2 \: _1} = 42cm$

Now, area is,

$\sf\tt\bf\large {\orange{\underbrace{\underline{A = \sqrt{S(S - a)(S - b)(S - c)} }}}}$

$\sf = \sqrt{42(42 - 28)(42 - 15)(42 - 41)} {}$

$\sf = \sqrt{42 \times 14 \times 27 \times 1} {}$

$\sf{ = \sqrt{15876} }$

$\sf \large \pink {\underbrace{\underline {\underbrace{= \: \: 126 {cm}^{2}}}}}$