Question

the perimeter of a Trapezium is 104 metre its non parallel sides are 18 M and 22 metre and its altitide is 16 metre find the area of a Trapezium

Answer 1

$given - \: \\ \\ \\ perimeter \: = 104 \\ sum \: of \: non \: parallel \: side \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 18 + 22 \\ \\ \: altitude \: \: \: \: = 16 \\ \\ \\ \\ \\ \\ \\ \\ let \: the \: parallel \: side \: be \: = {b}^{1} + {b}^{2} \\ \\ therefore \: perimeter \\ = non \: parallel \: side \: + parallel \: side \\ \\ \\ 104 = 18 + 22 + {b}^{1} + {b}^{2} \\ 104 = 40 + {b}^{1} + {b}^{2} \\ {b}^{1} + {b}^{2} = 104 - 40 \\ {b}^{1} + {b}^{2} = 64 \\ \\ \\ \\ \\ here \: area \: = \frac{1}{2} \times {b}^{1} + {b}^{2} \times altitude \\ \\ = \frac{1}{2} \times 64 \times 16 \\ \\ = 64 \times 8 \\ \\ 512$
therefore area is
$512 \: {m}^{2}$





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