Question

Q. The area of a trapezium is
400 cm?, the distance between
the parallel sides is 20 cm. If
one of the parallel sides is 30
cm, find the length of the other
side.​

Answer 1

$\mathfrak{ \large{ \orange{ \underline{ \pink{Correct \: Question: }}}}}$

The area of a trapezium is 400 cm², the distance between the parallel sides is 20 cm. If one of the parallel sides is 30 cm, find the length of the other side.

$\mathfrak{ \large{ \orange{ \underline{ \pink{Given: }}}}}$

• Area of trapezium = 400 cm²
• Height of trapezium = 20 cm
• First parallel side (a) = 30 cm

$\mathfrak{ \large{ \orange{ \underline{ \pink{To\: Find: }}}}}$

• Second parallel side

$\mathfrak{ \large{ \orange{ \underline{ \pink{Solution: }}}}}$

• Let the other parallel side be b

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \mathfrak{ \underline{ \green{Formula \: to \: calculate \: the \: area \: of \: trapezium}}}$

$\boxed { \boxed{ \star \: \: \: \: \: { \mathfrak{ \red{ \large{area = \frac{sum \: of \: parallel \: sides}{2} \times height}}}}}}$

According to question,

$\large{ \rm \longmapsto \: \: \: \: \: \: \: \: \: \frac{(30 + b)}{2} \times 20 = 400}$

$\large{ \rm \longmapsto \: \: \: \: \: \: \: \: \: (30 + b) \times 10 = 400}$

$\large{ \rm \longmapsto \: \: \: \: \: \: \: \: \: 30 + b = \frac{40 \cancel0}{1 \cancel0} }$

$\large{ \rm \longmapsto \: \: \: \: \: \: \: \: \: 30 + b = 40}$

$\large{ \rm \longmapsto \: \: \: \: \: \: \: \: \: b = 40 - 30}$

$\large{ \rm \longmapsto \: \: \: \: \: \: \: \: \boxed{ \boxed{ \mathfrak{ \purple{b = 10}}}}} \star$

$\mathfrak{ \large{ \orange{ \underline{ \pink{ Hence:}}}}}$

The length of another parallel side of trapezium is 10 cm.

Answer 2

$\bold{ Given \: that}\begin{cases} \sf \: Area \: of \: a \: trapezium \: = \: \bold{400 {cm}^{2}} \\ \\ \sf \: Distance \: between \: the \: parallel \: sides \: = \bold{20cm} \\ \\ \sf \: One \: of \: the \: parallel \: sides \: = \bold{30cm}\end{cases}$

$\sf\underline{We've \: to \: find \: the \: distance \: between \: the \: parallel \: sides.}$

________________________________

☯︎ Let other parallel side = a

$\sf\underline{As \: we \: know \: that : }$

$\boxed{\boxed{\sf\purple{area \: of \: a \: trapezium \: = \frac{1}{2} \times (sum \: of \: parallel \: sides) \times distance \: between \: them}}}$

Put the values :

$\sf:\implies \: area \: of \: the \: trapezium = \dfrac{1}{2} \times (30 + a) \times 30$$\sf:\implies \: 400 = \dfrac{1}{2} \times (30 + a) \times 20$

$\sf:\implies \: 400 = \cancel \dfrac{20}{2} \times (30 + a)$

$\sf:\implies \: 400 = 10(30 + a)$

$\sf:\implies \: \cancel\dfrac{400}{10} = 30 + a$

$\sf:\implies \: 40 = 30 + a$

$\sf:\implies \: a = 40 - 30$

$\sf:\implies \: a \: = \boxed{\boxed{\sf\purple{10 \: cm}}}\bigstar$

$\sf\therefore{\underline{Therefore, \: the \: other \: parallel \: side \: is \: \bold{10cm}.}}$