Question

Area of the trapezium is 177.24 millimeter square the dimension of two parallel sides are 28.9 millimetre and 13.3 millimetre find the distance between the parallel sides

Answer 1

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

$\bold{Given\:a\: trapezium}\begin{cases}\sf{Area=177.24mm{}^{2}}\\ \sf{parallel\:sides=28.9mm\:and\:13.3mm}\end{cases}$

$\large\bold{\red{To\:Find:-}}$

• we have to find the height of trapezium

• Now we know that the area of trapezium

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

$\sf\underline{\underline{\red{According\:to\: Question:-}}}$

$\sf\implies 177.24=\frac{1}{2}\times h\times (13.3+28.9)\\ \\ \sf \implies 177.24=\frac{1}{\cancel2}\times h\times \cancel{42.2}\\ \\ \sf\implies 177.24=21.1h\\ \\ \sf\implies \cancel{\frac{177.24}{21.1}}=h\\ \\ \sf\implies h=8.4$

$\boxed{\sf{Height=8.4mm}}$

• Now let's verify:-

$\bold{\underline{\red{Verification:-}}}$

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

$\bold{In\: trapezium}\begin{cases}\sf{Area=177.24mm{}^{2}}\\ \sf{parallel\:sides=28.9mm\:and\:13.3mm}\\ \sf{Height=8.4mm}\end{cases}$

$\sf 177.24mm{}^{2}=\frac{1}{2}\times 8.4mm\times(13.3+28.9)mm\\ \\ \sf\implies 177.24mm{}^{2}=\frac{1}{\cancel2}\times \cancel{8.4mm}\times 42.2mm\\ \\ \sf\implies 177.24mm{}^{2}= 4.2mm\times 42.2mm\\ \\ \sf\implies 177.24mm{}^{2}=177.24mm{}^{2}$

$\boxed{\red{\sf{Height=8.4mm}}}$

#BAL

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