Question

Area of Trapezium = 520 cm^2



Parallel Sides = 12 and 14 cm



Distance between them = ?


Find the value of height ?

Answer 1

$\sf \large\: Question:$

$\sf \green{ \: The \: \: parallel \: \: sides \: of \: \: a \: trapezium \: are \: 12 cm} \: \\ \sf \red{and \: 14 cm \: \: and \: area \: is \: 520cm^2 . find \: \: the} \: \: \\ \sf \blue{distance \: between \: \: the \: \: parallel \: sides ?}$

$\sf \large\:Method \: of \: Solution:$

$\sf {\green {Trapezium: Trapezium \: is \: a \: quadrilateral \: \: means \: \: four \: \: sided}} \\ \: \sf{\red {closed\: \: figure \: \: in \: \: \: which \: a \: pair \: of \: \: opposite \: \: sides \: \: are \: \: parallel.}}$

$\sf {\small{ \green{Area \: of \: Trapezium = \: \sf{ \red{(Sum \: of \: Parallel \: Side) \times}} \sf{ \blue{ (Distance \: between \: Them)\: \div 2}}}}} \\ \\ \\ \implies{ \sf {\small{ \green{1040 {cm}^{2}}}}} = \sf{ \red{ \small{(12+ 14)}}} \times { \sf{(Distance \: between \: Them)}} \\ \\ \\ \implies{ \sf {\small{ \green{1040 {cm}^{2}}}}} =( 26 cm) \times{ { \sf{(Distance \: between \: Them)}}} \\ \\ \\ \implies{ \sf{ \red{(Distance \: between \: Them)}}} = \cancel{ \green{\frac{1040.00}{26.00}}} \\ \\ \\ \\ \implies{ \sf{ \blue{(Distance \: between \: Them)}}} = \sf{ \fbox{ \red{40 \: cm}}} \\ \\ \\ \\ \sf{ \green{ \fbox{ \blue{Hence,} \: Required \: \red{Distance \: \: Between \: them} \: \: = 40cm}}}$

Answer 2

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SOLUTION:-




STEP BY STEP EXPLAINATION




Let the height be x cm



NOW ATQ,



AREA OF TRAPEZIUM=520cm(GIVEN)


Side1=12cm(GIVEN)


Side2=14cm(GIVEN)



AREA OF TRAPEZIUM=1/2×sum of parallel sides×height


$520 = 1 \div 2(12 + 14) \times x$


$520 = 1 \div 2 \times 26 \times x$


$x = 520 \div 13$



$x = 40$


THEREFORE,



HEIGHT OF TRAPEZIUM=40cm



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