The sides of Delta PQR measure 13 , cm, 14 , | vedclass

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Question

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

Vedclass · Accepted Answer

$84$

Vedclass · Answer

(C) Given sides of the triangle are $a = 13 \, cm$, $b = 14 \, cm$, and $c = 15 \, cm$.First, calculate the semi-perimeter $(s)$:$s = \frac{a + b + c}{2} = \frac{13 + 14 + 15}{2} = \frac{42}{2} = 21 \, cm$.Now, use Heron's formula for the area of the triangle:$	ext{Area} = \sqrt{s(s - a)(s - b)(s - c)}$$	ext{Area} = \sqrt{21(21 - 13)(21 - 14)(21 - 15)}$$	ext{Area} = \sqrt{21 	imes 8 	imes 7 	imes 6}$$	ext{Area} = \sqrt{(3 	imes 7) 	imes (2^3) 	imes 7 	imes (2 	imes 3)}$$	ext{Area} = \sqrt{2^4 	imes 3^2 	imes 7^2}$$	ext{Area} = 2^2 	imes 3 	imes 7 = 4 	imes 21 = 84 \, cm^2$.

The sides of $\Delta PQR$ measure $13 \, cm$, $14 \, cm$, and $15 \, cm$. Find its area in $cm^2$.

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