Question

4.
If the area of a trapezium is 28 m?, and two parallel sides are 8 m and 60 dm
respectively, find the altitude.
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Answer 1

Given : Area of a trapezium is 28m² and two parallel sides are 8m and 60m respectively.

To Find : Altitude of the trapezium.

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Here

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• Area of the trapezium is 28m²
• Two parallel sides of the trapezium are 8m and 60dm (60dm = 6m)

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As we know that :

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$\underline{\boxed{\tt\purple{\bigstar \: area \: of \: a \: trapezium \: = \frac{1}{2} \times sum \: of \: parallel \: sides \: \times altitude}}}$

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Now, we'll find the altitude of the trapezium by putting the values of given information.

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Put the values and solve -

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$\tt:\implies \: area \: of \: the \: trapezium \: = \dfrac{1}{2} \times sum \: of \: parallel \: sides \: \times altitude \\ \\ \\ \tt:\implies \: 28 = \frac{1}{2} \times (8 + 6) \times altitude \\ \\ \\ \tt:\implies \: 28 = \cancel\frac{14}{2} \times altitude \\ \\ \\ \tt:\implies \: 28 = 7 \times altitude \\ \\ \\ \tt:\implies \: altitude \: = \cancel\frac{28}{7} \\ \\ \\ \tt:\implies \: altitude \: = \underline{\boxed{\tt\purple{4m}}}\bigstar \\ \\ \\ \\ \sf\therefore{\underline{Hence, \: the \: altitude \: of \: the \: trapezium \: is \: \bold{4m}}}$