Question

the area of trapezium is 216 square CM the length of its parallel sides are 14 cm and 22 cm what is the distance between the parallel sides​

Answer 1

Step-by-step explanation:

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Answer 2

$\frak{Given}\begin{cases} \sf{ The\:Area\:of\:Trapezium \:is\:216cm^{2}}\\\\\sf{Two\:Parallel \:Sides\:of\:Trapezium \:are\:14cm\:\&\:22cm}\end{cases}$

Need to find: The other parallel side.

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$\underline{\frak{Diagram:}}$

$\setlength{\unitlength}{1.1cm}\begin{picture}(0,0)\thicklines\qbezier(0,0)(0,0)(1,2.2)\qbezier(0,0)(0,0)(4,0)\qbezier(3,2.2)(4,0)(4,0)\qbezier(1.5,2.2)(0,2.2)(3,2.2)\put(0.8,2.4){ \bf A }\put(3,2.4){ \bf B }\put(-0.3,-0.3){ \bf D }\put(4,-0.3){ \bf C }\put(4.4,0){\vector(0,0){2.2}}\put( 4.4, 0){\vector(0,-1){0.1}}\put(4.6,1){ \bf ?\ cm }\put(0, -0.5){\vector(1,0){4}}\put(0, -0.5){\vector( - 1, 0){0.1}}\put(1.7, - 0.9){ \bf 14\ cm }\put(0.8, 2.8){\vector(1,0){2.5}}\put(0.8, 2.8){\vector( - 1, 0){0.1}}\put(1.7, 3){ \bf 22\ cm }\end{picture}$ ⠀⠀

❍ Let the distance between parallel side or Height of the trapezium be h cm respectively.

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

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

Where,

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

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

$:\implies\sf 216 = \dfrac{1}{2}(14 + 22) \times h \\\\\\:\implies\sf 216 \times 2 = (14+ 22)\times h \\\\\\:\implies\sf 432 = (14 + 22) \times h\\\\\\:\implies\sf 432 = 36\times h\\\\\\ :\implies\sf h = \cancel\dfrac{432}{36}\\\\\\:\implies{\underline{\boxed{\frak{\pink{h = 12\;cm}}}}}\;\bigstar$

$\therefore{\underline{\sf{Hence, \;the\;Height \; of\;Trapezium \;is\;\bf{ 12\;cm}.}}}.$

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