Find the area of a triangle whose sides are 1 | vedclass

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(D) Let the sides of the triangle be $a = 13\, cm$,$b = 14\, cm$,and $c = 15\, cm$.First,calculate the semi-perimeter $s$:$s = \frac{a + b + c}{2} = \

Vedclass · Accepted Answer

$84$

Vedclass · Answer

(D) Let the sides of the triangle be $a = 13\, cm$,$b = 14\, cm$,and $c = 15\, cm$.First,calculate the semi-perimeter $s$:$s = \frac{a + b + c}{2} = \frac{13 + 14 + 15}{2} = \frac{42}{2} = 21\, cm$.Using Heron's formula,the area of the triangle is given by $\sqrt{s(s - a)(s - b)(s - c)}$.Area $= \sqrt{21(21 - 13)(21 - 14)(21 - 15)}$Area $= \sqrt{21 	imes 8 	imes 7 	imes 6}$Area $= \sqrt{(3 	imes 7) 	imes (2^3) 	imes 7 	imes (2 	imes 3)}$Area $= \sqrt{3^2 	imes 7^2 	imes 2^4}$Area $= 3 	imes 7 	imes 2^2 = 21 	imes 4 = 84\, cm^2$.

Find the area of a triangle whose sides are $13\, cm$,$14\, cm$,and $15\, cm$. (in $, cm^2$)

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