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Question

# If the area of a trapezium is 28 cm2 and one of its parallel sides is 6 cm, find the other parallel side if its altitude is 4 cm.

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Solution

## $\text{Given:}\phantom{\rule{0ex}{0ex}}{\text{Area of the trapezium = 28 cm}}^{2}\phantom{\rule{0ex}{0ex}}\mathrm{L}\text{ength of one of its parallel sides = 6 cm}\phantom{\rule{0ex}{0ex}}\text{Altitude = 4 cm}\phantom{\rule{0ex}{0ex}}\text{Let the other side be x cm.}\phantom{\rule{0ex}{0ex}}\text{Area of trapezium=}\frac{1}{2}\text{×(Sum of the parallel sides)×(Altitude)}\phantom{\rule{0ex}{0ex}}⇒\text{28=}\frac{1}{2}\text{×(6+x)×(4)}\phantom{\rule{0ex}{0ex}}⇒28=2×\left(6+\text{x)}\phantom{\rule{0ex}{0ex}}⇒\text{6+x=}\frac{28}{2}\text{=14}\phantom{\rule{0ex}{0ex}}⇒\text{x=14-6=8 cm}\phantom{\rule{0ex}{0ex}}\text{Hence, the length of the other parallel side of the trapezium is 8 cm.}$

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