Question

The Area Of A Trapezium is 45 cm2 and the perpendicular distance between its parallel
Sides Is 5 cm. If The Length Of One Parallel sides is 6cm.Find The Length of the other parallel side

Answer 1

$\huge\sf\pink{Answer}$

☞ The length of the other parallel side = 12 cm

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$\huge\sf\blue{Given}$

➝ Area of a trapezium = 45 cm²

➝ Perpendicular distance b/w parallel sides = 5 cm

➝ Length of one parallel side = 6 cm

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$\huge\sf\gray{To \:Find}$

✭ The of the other parallel side?

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$\huge\sf\purple{Steps}$

$\normalsize\bullet\:\sf\ Area \: of \: Trapezium = \bf\ 45cm^2$

$\normalsize\bullet\:\sf\ Perpendicular \: distance \: or \: Height(h) = \bf\ 5cm$

$\normalsize\bullet\:\sf\ One \: of \: the \: parallel \: side(a) = \bf\ 6cm$

$\normalsize\bullet\:\sf\ Let \: the \: second \: parallel \: side \: be \:\bf\ x \: cm$

$\underline{\bigstar\:\textsf{As\:per\:the\:Question:}}$

$\normalsize{\boxed{\sf{ \green{Area \: of \: Trapezium = \frac{1}{2} \times\ (Sum \: of \: \parallel\ \: sides)}}}}$

$\normalsize \dashrightarrow\quad\sf\ 45 \: = \: \frac{1}{2} \times\ (6 + x) \times\ 5$

$\normalsize\dashrightarrow\quad\sf\dfrac{{45} \times\ 2}{{5}} \: = (6 + x)$

$\normalsize \dashrightarrow\quad\sf\ 9 \times\ 2 \: = \: (6 + x)$

$\normalsize\dashrightarrow\quad\sf\ 18 \: = \: \ 6 + x$

$\normalsize \dashrightarrow\quad\sf\ x \: = \: 18 - 6$

$\normalsize\orange{\dashrightarrow\quad\sf\ x = 12}$

$\rule{170}3$

Answer 2

Answer:

The length of the other parallel side is 12cm.

Step-by-step explanation:

Given the area of a trapezium, $A= 45 cm^2$

The perpendicular distance between the parallel sides, h = 5 cm

The length of one of the parallel sides, a = 6cm

Area of a trapezium is given by

$A= \dfrac{1}{2} (a+b)h$

where a and b are the lengths of the parallel sides respectively, and h is the perpendicular distance between the parallel sides.

Substituting the given values in the formula of area of trapezium,

$45= \dfrac{1}{2} (6+b)5$

$\implies45\times 2= (6+b)5\implies\dfrac{45\times 2}{5} = 6+b$

$\implies9\times 2= 6+b\implies b=18- 6=12cm$

Therefore, the length of the other parallel side is 12cm.

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