Question

Two parallel sides of a trapezium are 16cm and 20cm. If its area is equal to 90cm then what is the height of the trapezium?​

Answer 1

Given: Two ∥ sides of the trapezium are 16cm and 29cm and the area of the trapezium is 90cm².

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Need to find: The height of the trapezium.

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⋆ DIAGRAM:

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$\setlength{\unitlength}{1.1cm}\begin{picture}(0,0)\thicklines\qbezier(0,0)(0,0)(1,2.2)\qbezier(0,0)(0,0)(4,0)\qbezier(3,2.2)(4,0)(4,0)\qbezier(1.5,2.2)(0,2.2)(3,2.2)\put(0.8,2.4){ \bf A }\put(3,2.4){ \bf D }\put(-0.3,-0.3){ \bf B }\put(4,-0.3){ \bf C }\put(4.4,0){\vector(0,0){2.2}}\put( 4.4, 0){\vector(0,-1){0.1}}\put(4.6,1){ \sf h \ cm }\put(0, -0.5){\vector(1,0){4}}\put(0, -0.5){\vector( - 1, 0){0.1}}\put(1.7, - 0.9){ \sf 20\ cm }\put(0.8, 2.8){\vector(1,0){2.5}}\put(0.8, 2.8){\vector( - 1, 0){0.1}}\put(1.7, 3){ \sf 16\ cm }\end{picture}$

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

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★ To calculate the area of trapezium formula is given by :

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

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where,

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• a and b are the two ∥ sides, h is distance between two ∥ sides or height and area of the trapezium is given that is 90cm².

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Therefore,

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$\sf{⇢\;90=\dfrac{1}{2}\times (16+20)\times h}\\\\\\\sf{⇢\;90=\dfrac{1}{2}\times 36\times h}\\\\\\\sf{⇢\;90=18\times h}\\\\\\\sf{⇢\;h=\cancel{\dfrac{90}{18}}}\\\\\\⇢\;{\underline{\boxed{\purple{\frak{h=5\;cm}}}}}{\;\bigstar}$

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$\therefore\;{\underline{\sf{Hence,\;the\; height\;of\;the\; trapezium\;is\;{\textsf{\textbf{5\;cm}}}}.}}$

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Answer 2

the height of the trapezium is 5cm.