Question

Hence, the sum of the parelle sides of the tapezium 64 cm area
of the trepezium is 320m3, then find the height of the trapezium​

Answer 1

$\mathfrak{Given}\begin{cases} \sf \: Sum \: of \: two \: parallel \: sides \: of \: a \: trapezium \: is \: \bold{64 \: cm}. \\ \\ \sf \: Area \: of \: the \: trapezium \: is \: \bold{320 \: cm {}^{2} }.\end{cases}$

Need to find : height of the trapezium.

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$\: \:$

For finding the area of the trapezium, formula is given as :

$\: \:$

$\star \: \underline{\boxed{\sf\purple{Area_{(trapezium)} = \frac{1}{2} \times sum \: of \: parallel \: sides \: \times height}}}$

$\: \:$

$\mathfrak{ \underline{Substituting \: the \: values \: : }}$

$\: \:$

$\sf:\implies \: Area_{(trapezium)} = \frac{1}{2} \times sum \: of \: parallel \: sides \: \times height \\ \\ \\ \sf:\implies \: 320 = \frac{1}{2} \times 64 \times height \\ \\ \\ \sf:\implies \: 320 = 32 \times height \\ \\ \\ \sf:\implies \: height \: = \cancel\frac{320}{32} \\ \\ \\ \sf:\implies \: \underline{\boxed{\mathfrak\pink{height = 10 \: cm}}} \: \bigstar \\ \\ \\ \\ \sf\therefore{\underline{Hence, \: the \: height \: of \: the \: trapezium \: is \: \bold{10 \: cm}.}}$

Answer 2

Correct Question:

The sum of the parallel sides of the trapezium is 64 cm and the area of the trapezium is 320 cm², then find the height of the trapezium.

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Given:

For trapezium,

1. Sum of parallel sides = 64 cm
2. Area = 320 cm²

To find:

• The height of the trapezium.

Solution:

$\boxed{\tt{\red{Area_{(trapezium)}}=\dfrac{1}{2}\times \ Sum \ of \ parallel \ sides\times \ Height}}$

$\rm{\leadsto{320=\dfrac{1}{2}\times64\times \ \purple{h}}}$

$\rm{\therefore{\purple{h}= 10 \ cm}}$

Therefore, the height of the trapezium is 10 cm.