Question

The area of a trapezium is 34sq.cm. And the length of one of

The parallel sides is 10cm and its height is 4cm.

Find the length of the another parallel sides.

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Answer 1

$\frak{Given}\begin{cases} \sf{ The\:Area\:of\:Trapezium \:is\:34cm^{2}}\\\sf{The \:Distance \:between \:\parallel \:or\:Height \:is\:4cm\:}\\\sf{One\:Parallel \:Side\:of\:Trapezium \:is\:10cm}\end{cases}$

Need to find: The other parallel side.

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❍ Let the one of the parallel side of the trapezium be b cm respectively.

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

$\setlength{\unitlength}{1.1cm}\begin{picture}(0,0)\thicklines\qbezier(0,0)(0,0)(1,2.2)\qbezier(0,0)(0,0)(4,0)\qbezier(3,2.2)(4,0)(4,0)\qbezier(1.5,2.2)(0,2.2)(3,2.2)\put(0.8,2.4){ \bf A }\put(3,2.4){ \bf B }\put(-0.3,-0.3){ \bf D }\put(4,-0.3){ \bf C }\put(4.4,0){\vector(0,0){2.2}}\put( 4.4, 0){\vector(0,-1){0.1}}\put(4.6,1){ \bf 4\ cm }\put(0, -0.5){\vector(1,0){4}}\put(0, -0.5){\vector( - 1, 0){0.1}}\put(1.7, - 0.9){ \bf 10\ cm }\put(0.8, 2.8){\vector(1,0){2.5}}\put(0.8, 2.8){\vector( - 1, 0){0.1}}\put(1.7, 3){ \bf ?\ cm }\end{picture}$ ⠀⠀

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

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

Where,

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

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

$:\implies\sf 34 = \dfrac{1}{2}(10 + b) \times 4 \\\\\\:\implies\sf 34 \times 2 = (10 + b)\times 4 \\\\\\:\implies\sf 68 = (10 + b) \times 4\\\\\\:\implies\sf 68 = 40 + 4b\\\\\\:\implies\sf 68 - 40 = 4b\\\\\\:\implies\sf 28 = 4b \\\\\\:\implies\sf b = \cancel\dfrac{28}{4}\\\\\\:\implies{\underline{\boxed{\frak{\pink{b = 7\;cm}}}}}\;\bigstar$

$\therefore{\underline{\sf{Hence, \;the\;other\; parallel\;side\;is\;\bf{ 7\;cm}.}}}.$

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