Question

the area of trapezium is 182 CM square its height 14 cm the larger parallel side is longer than other by 16 centimetre find the find the length of the parallel sides

Answer 1

let the upper parellal side be x
other side =x+16 cm

$area \: of \: parellalogram \\ = \frac{1}{2} h(a + b) \\where \: a \: and \: b \: \\ are \: sum \: of \: parellal \: sides$
therefore

$182 = \frac{1}{2}14(x + x + 16)$
$182 = \frac{1}{2}14 (2x + 16)$
$182 \times 2 \times \frac{1}{14} = 2x + 16$
$26 = 2x + 16$
$26 - 16 = 2x$
$10 = 2x$
$x = \frac{10}{2}$
$x = 5$
therefore,

the shorter parellal side=5cm
the base of the parellalogram=5+16=21 cm

Answer 2

182=1/2*14(x+x+16)

182=1/2*14(2x+16)

182=2×1/14=2x+16

26=2x+16

26-16=2x

10=2x

x=10/2

x=5

the base of the parallogram=5+16=21cm