Question

The area of a Trapezium is 180m square if its two parallel side are 21 metre and 15 metre find the distance between the parallel sides area of trapezium is 180 metre square if its two parallel side are 21 and 15 metre find the distance between the parallel side

Answer 1

Answer:

Area of trapezium = 1/2 (h) (b1+b2)

180 = 1/2 (h) (21+15)

180×2 = h×36

360 = h×36

h = 360/36

h = 10 m

Distance between the parallel sides is 10 m.

#WMK

Answer 2

Given:

• Area of trapezium = 180 m².
• Two parallel sides of trapezium are 21 m and 15 m.

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To find:

• The distance between the parallel side.

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀

☯ Let the distance between two parallel sides i.e. height be h cm.

$\setlength{\unitlength}{1.4cm}\begin{picture}(0,0)\thicklines\qbezier(0,0)(0,0)(1,2.2)\qbezier(0,0)(0,0)(4,0)\qbezier(3,2.2)(4,0)(4,0)\qbezier(1.5,2.2)(0,2.2)(3,2.2)\put(0.8,2.4){ \bf A }\put(3,2.4){ \bf D }\put(-0.3,-0.3){ \bf B }\put(4,-0.3){ \bf C }\put(4.4,0){\vector(0,0){2.2}}\put( 4.4, 0){\vector(0,-1){0.1}}\put(4.6,1){ \bf h\ m }\put(0, -0.5){\vector(1,0){4}}\put(0, -0.5){\vector( - 1, 0){0.1}}\put(1.7, - 0.9){ \bf 21\ m }\put(0.8, 2.8){\vector(1,0){2.5}}\put(0.8, 2.8){\vector( - 1, 0){0.1}}\put(1.7, 3){ \bf 15\ m }\end{picture}$

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

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

Where

⠀⠀⠀⠀

• a & b are parallel sides
• h is the height or distance between two parallel sides

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

$:\implies\sf \dfrac{1}{2} \times (15 + 21) \times h = 180$

$:\implies\sf \dfrac{1}{2} \times 36 \times h = 180$

$:\implies\sf 36 \times h = 180 \times 2$

$:\implies\sf 36 \times h = 360$

$:\implies\sf h = \cancel{ \dfrac{360}{36}}$

$:\implies{\underline{\boxed{\frak{\purple{h = 10\:m}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Hence,\:the\:distance\;between\:two\: parallel\:sides\:is\: {\textsf{\textbf{10\:m}}}.}}}$