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 of its parallel sides is 6 cm, find the length of the other parallel side.​

Answer 1

⋆Reference of image is in attachment

AnswEr :

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

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

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

$\rule{170}2$

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

$\underline{\bigstar\:\textsf{According \: to \: given \: in \: Question:}}$

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

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

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

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

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

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

$\normalsize\ : \implies\quad\sf\ x = 12$

$\therefore\:\underline{\textsf{Hence, \: the \: other \: parallel \: side \: is}{\textbf{\: 12cm }}}$

$\rule{170}1$

$\boxed{\begin{minipage}{8cm}\bf\underline{Some important formula related to it :}\\ \\ \textsf{ \bullet\ Perimeter \: of \: rectangle = 2(length + breadth) }\\ \textsf{ \bullet\ Area \: of \: rectangle = length \times\ breadth } \\ \textsf{ \bullet\ Area \: of \: square = (side)^2 } \\ \textsf{ \bullet\ Perimeter \: of \: square = 4 \times\ side } \\ \textsf{ \bullet\ Area \: of \: circle = \pi r^2 }\\ \textsf{ \bullet\ Circumference \: of \: circle = 2 \pi r }\\ \textsf{ \bullet\ Area \: of \: triangle= \sqrt{s(s-a)(s-b)(s-c)} }\\ \textsf{ \bullet\ Perimeter \: of \: triangle = sum \: of \: sides(a + b + c) }\end{minipage}}$

Answer 2

Answer:

★ 12 cm ★

Step-by-step explanation:

Given:

• Area of trapezium is 45 cm²
• Distance between its parallel sides is 5 cm
• Length of one parallel side is 6 cm

To Find:

• Length of another parallel side

Solution: Let the length of another parallel side be y cm.

★ Area of Trapezium= 1/2( Sum of parallel sides)(Distance between them)

$\small\implies{\sf }$ 45 = 1/2( 6 + y ) (5)

$\small\implies{\sf }$ 45 x 2 = 30 + 5y

$\small\implies{\sf }$ 90 –30 = 5y

$\small\implies{\sf }$ 60 =5y

$\small\implies{\sf }$ 60/5 = y

$\small\implies{\sf }$ 12 cm = y

Hence , The Length of another Parallel Side of trapezium = y = 12 cm.