Question

area of a triangle whos sides are 40m,24m,32m by herons formula
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Answer 1

Answer:

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Answer 2

Given :-

• Side a = 40m
• side b = 24 m
• side c = 32 m

To find :-

• Area of the triangle by using heron's formula

Solution :-

Finding semi - perimeter

$\mathsf{Semi-perimeter\:=\:\dfrac{a\:+\:b\:+\:c}{2}}$

$\mathsf{Semi-perimeter\:=\:\dfrac{40\:+\:24\:+\:32}{2}}$

$\mathsf{Semi-perimeter\:=\:\dfrac{96}{2}}$

$\mathsf{Semi-perimeter\:=\:48m}$

$\mathsf{\therefore\:Semi-perimeter\:is\:48m}$

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Finding area of the triangle

$\mathsf{Area\:of\:triangle\:=\:\sqrt{S(s-a)\:(s-b)\:(s-c)} }$

Where ,

• S = semi - perimeter
• a = length of side a
• b = length of side b
• c = length of side c

$\mathsf{Area\:of\:triangle\:=\:\sqrt{48(48-40)\:(48-24)\:(48-32)} }$

$\mathsf{Area\:of\:triangle\:=\:\sqrt{48(8)\:(24)\:(16)} }$

$\mathsf{Area\:of\:triangle\:=\:\sqrt{24\times2\times24\times8\times8\times2} }$

$\mathsf{Area\:of\:triangle\:=\:24\times8\times2 }$

$\mathsf{Area\:of\:triangle\:=\:384m^{2}}$

$\red{\mathsf{\therefore\:Area\:of\:the\:triangle\:is\:384\:m^{2}}}$