Question

the area of a trapezium is 40cm² it's parallel sides are 12cm and 8cm the distance between the parallel sides is ​

Answer 1

$\frak{Given} \begin{cases} & \sf{Area\:of\: trapezium = \bf{40\:cm^2}} \\ & \sf{One\:side\:of\:trapezium = \bf{12\:cm}} \\ & \sf{Other\:side\:of\:trapezium = \bf{8\:cm}} \end{cases}$

$\frak{To\:find:}$ The distance between parallel sides?

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

☯ Let the distance between two parallel sides be x cm.

⠀⠀⠀⠀

⋆ DIAGRAM

$\setlength{\unitlength}{1.1cm}\begin{picture}(0,0)\thicklines\qbezier(0,0)(0,0)(1,2.2)\qbezier(0,0)(0,0)(4,0)\qbezier(3,2.2)(4,0)(4,0)\qbezier(1.5,2.2)(0,2.2)(3,2.2)\put(0.8,2.4){ \bf A }\put(3,2.4){ \bf D }\put(-0.3,-0.3){ \bf B }\put(4,-0.3){ \bf C }\put(4.4,0){\vector(0,0){2.2}}\put( 4.4, 0){\vector(0,-1){0.1}}\put(4.6,1){ \bf x\ cm }\put(0, -0.5){\vector(1,0){4}}\put(0, -0.5){\vector( - 1, 0){0.1}}\put(1.7, - 0.9){ \bf 12\ cm }\put(0.8, 2.8){\vector(1,0){2.5}}\put(0.8, 2.8){\vector( - 1, 0){0.1}}\put(1.7, 3){ \bf 8\ cm }\end{picture}$

⠀⠀⠀⠀

$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

The Area of trapezium is given by,

$\star\;{\boxed{\sf{\pink{Area_{\;(trapezium)} = \dfrac{1}{2} \times (a + b) \times h}}}}$

Where,

• a and b are the two parallel sides and h is distance between two parallel sides or height of trapezium.

⠀⠀⠀⠀

$\dag\;{\underline{\frak{Now,\: Substituting\:values\:in\;formula,}}}$

$:\implies\sf 40 = \dfrac{1}{2} \times (12 + 8) \times x\\ \\ \\:\implies\sf 40 = \dfrac{1}{ \cancel{2}} \times \cancel{20} \times x\\ \\ \\:\implies\sf 40 = 10 \times x\\ \\ \\ :\implies\sf x = \cancel{ \dfrac{40}{10}}\\ \\ \\ :\implies{\underline{\boxed{\frak{\purple{x = 4\:cm}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Hence,\:The\:distance\:between\:two\: parallel\: sides\:is\: {\textsf{\textbf{4\:cm}}}.}}}$

Answer 2

Step-by-step explanation:

area of trapezium is 40cm sq.

formula of area of trapezium is 1/2×(sum of the parallel sides)×height

now cancel out

h is the distance between the parallel sides