Question

$\huge \tt{ \pink {☆Question}}$
The area of a trapezium is 34 cm² and the length of one of the parallel side is 10cm and its height is 4cm. Find the length of the parallel side.​

Answer 1

Answer:

Length of other parallel sides = 7 cm

Step-by-step explanation:

Given :

Area of the trapezium = 34cm²

Length of one of its parallel side = 10 cm

Height = 4 cm

To find :

Length of the other parallel side

Taken :

Let the other parallel side be x

To find the length of the other parallel side use this formula -:

$\boxed{\rm{A=\dfrac{1}{2}\times\:S\times\:h}}$

Where,

A = Area of the trapezium

S = Sum of its parallel side

h = Height

Solution :

$:\implies\rm{{34cm}^{2}=\dfrac{1}{2}\times(10cm+x)\times4cm}$

$:\implies\rm{\cancel{\dfrac{{34cm}^{2}\times2}{4cm}}=10cm+x}$

$:\implies\rm{17cm=10cm+x}$

$:\implies\rm{17cm-10cm=x}$

$:\implies\rm{7cm=x}$

So , the length of other parallel side of the trapezium is 7 cm .....

Answer 2

$\sf Given \begin{cases} & \sf{Area\:of\: trapezium = \bf{34\:cm^2}} \\ & \sf{Length\:of\:one\:parallel\:side = \bf{10\:cm}} \\&\sf{Height\:of\:trapezium = \bf{4\:cm}} \end{cases}$

To find: Length of other parallel side?

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

☯ Let's consider the length of other parallel side be x cm.

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DIAGRAM:

$\setlength{\unitlength}{1.3cm}\begin{picture}(0,0)\thicklines\qbezier(0,0)(0,0)(1,2.2)\qbezier(0,0)(0,0)(4,0)\qbezier(3,2.2)(4,0)(4,0)\qbezier(1.5,2.2)(0,2.2)(3,2.2)\put(0.8,2.4){ \bf A }\put(3,2.4){ \bf D }\put(-0.3,-0.3){ \bf B }\put(4,-0.3){ \bf C }\put(4.4,0){\vector(0,0){2.2}}\put( 4.4, 0){\vector(0,-1){0.1}}\put(4.6,1){ \bf 4\ cm }\put(0, -0.5){\vector(1,0){4}}\put(0, -0.5){\vector( - 1, 0){0.1}}\put(1.7, - 0.9){ \bf 10\ cm }\put(0.8, 2.8){\vector(1,0){2.5}}\put(0.8, 2.8){\vector( - 1, 0){0.1}}\put(1.7, 3){ \bf x\ cm }\end{picture}$

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

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 two parallel sides & h is the height or distance between two parallel sides of trapezium.

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$:\implies\sf 34 = \dfrac{1}{2} \times (10 + x) \times 4\\ \\ \\ :\implies\sf 34 = \dfrac{1}{\cancel{2}} \times (10 + x) \times \cancel{4}\\ \\ \\ :\implies\sf 34 = (10 + x) \times 2\\ \\ \\ :\implies\sf 34 = 20 + 2x\\ \\ \\ :\implies\sf 34 - 20 = 2x\\ \\ \\:\implies\sf 14 = 2x\\ \\ \\ :\implies\sf x = \cancel{\dfrac{14}{2}}\\ \\ \\:\implies{\underline{\boxed{\frak{\purple{x = 7\:cm}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Hence,\:Length\:of\:other\:side\:is\: {\textsf{\textbf{7\:cm}}}.}}}$