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(B) Step $1$: Calculate the semi-perimeter $(s)$ of the triangle with sides $a = 10 \, cm$,$b = 17 \, cm$,and $c = 21 \, cm$.$s = (a + b + c) / 2 = (1

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$7$

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(B) Step $1$: Calculate the semi-perimeter $(s)$ of the triangle with sides $a = 10 \, cm$,$b = 17 \, cm$,and $c = 21 \, cm$.$s = (a + b + c) / 2 = (10 + 17 + 21) / 2 = 48 / 2 = 24 \, cm$.Step $2$: Calculate the area of the triangle using Heron's formula: $	ext{Area} = \sqrt{s(s-a)(s-b)(s-c)}$.$	ext{Area} = \sqrt{24(24-10)(24-17)(24-21)} = \sqrt{24 	imes 14 	imes 7 	imes 3} = \sqrt{7056} = 84 \, cm^2$.Step $3$: The area of the parallelogram is equal to the area of the triangle,so $	ext{Area} = 84 \, cm^2$.The formula for the area of a parallelogram is $	ext{base} 	imes 	ext{height}$.Given $	ext{base} = 12 \, cm$,we have $12 	imes 	ext{height} = 84$.$	ext{height} = 84 / 12 = 7 \, cm$.

$A$ triangle and a parallelogram have the same area. If the sides of the triangle are $10 \, cm$,$17 \, cm$,and $21 \, cm$,and the parallelogram stands on the base $12 \, cm$,find the height of the parallelogram. (in $, cm$)

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