Question

The area of a trapezium is 168cm². If the length of parallel sides are 36m and 20m. Find the height​

Answer 1

$\boxed{\sf{Correct\: Question}}$

The area of a trapezium is 168m². If the length of parallel sides are 36m and 20m. Find the height

$\huge\mathbb{\pink{SOLUTION:-}}$

$\bold{Given}\begin{cases}\sf{Area\:of\: trapezium=168cm{}^{2}}\\ \sf{parallel\:sides=36m\:and\:20m}\end{cases}$

$\boxed{\sf{Area\:of\: trapezium=\frac{1}{2}\times (sum\:of\: parallel\:sides)\times Height}}$

• Let the height be x

$\bf\underline{\underline{According\:to\: question:-}}$

$\sf Area=\frac{1}{2}\times (sum\:of\:parallel\:sides)\times h\\ \\ \sf\implies 168m{}^{2}=\frac{1}{2}\times (36+20)\times x\\ \\ \sf\implies 168m{}^{2}=\frac{1}{\cancel2}\times \cancel{56m}\times x\\ \\ \sf\implies 168m{}^{2}=28m\times x\\ \\ \sf\implies \cancel{\frac{168m{}^{2}}{28m}}=x \\ \\ \sf\implies 6=x\\ \\ \sf\implies height=6m$

• The height of trapezium is 6m

$\boxed{\sf{\purple{Verification:-}}}$

$\sf Area=\frac{1}{2}\times (sum\:of\:parallel\:side)\times h$

$\bold{we\:have}\begin{cases}\sf{Area\:of\: trapezium=168cm{}^{2}}\\ \sf{parallel\:sides=36m\:and\:20m}\\ \sf{Height=6m}\end{cases}$

$\sf\implies 168=\frac{1}{2}\times (36+20)\times 6\\ \\ \sf\implies 168=\frac{1}{\cancel2}\times \cancel{56}\times 6\\ \\ \sf\implies 168=28\times 6\\ \\ \sf\implies 168=168\\ \\ \sf\leadsto L.H.S=R.H.S\:\:\:\:\:\:\bf Hence\: verified$

$\boxed{\mathfrak{Height=6m}}$

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