Question

give derivation of heron's formula

Answer 1

according to properties of triangle ,
sinA/2 = √{(s -b)(s -c)/bc }
cosA/2 =√{s (s - a)/bc}

ar∆ = 1/2bc.sinA = 1/2casinB = 1/2absinC

ar∆ = 1/2bcsinA

= 1/2bc (2sinA/2.cosA/2)

put above value ,

ar∆ = 1/2bc { 2√s(s-a)(s-b)(s-c)/b²c²}
=√s(s-a)(s-b)(s-c)
hence proved

Answer 2

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$\bf\Huge\red{\mid{\overline{\underline{ ANSWER }}}\mid }$

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$\Large\fbox{\color{purple}{QUESTION}}$

DERIVATION OF THE HERON'S FORMULA

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$\Large\fbox{\color{purple}{ SOLUTION }}$

$\Large\mathcal\orange{HERON'S \: FORMULA }$

$\mathfrak\pink{\implies let \: semi \: perimeter \: = x</p><p>}$

$\mathfrak\pink{\implies x = \frac{a \: + \: b + c \: }{2}}$

$\mathfrak\red{area \: of \: triangle \: by \: herons \: formula}$

$\mathfrak\red{\implies\sqrt{x(x - a)(x - b)(x - c) \: } }$

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