Verified answer

Given :

• The Area of trapezium of height 24.2 cm is 605 cm². One of the parrallel sides is 21 cm.

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To Find :

• Other side of trapezium ?

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[tex]{\rule{190pt}{2pt}}[/tex]

SolutioN :

• Let us assume that, the other side be x cm.

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[tex]{\bf{\dag}}[/tex] Formula Used :

[tex]\qquad\star~{\underline{\boxed{\pmb{\sf{Area_{(Trapezium)}~=~\dfrac{1}{2}~×~(Sum~of~ Parallel~Sides)~×~ Height}}}}}[/tex]

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[tex]{\bf{\dag}}[/tex] According to the Question :

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[tex]\qquad{\sf:\implies{Area_{(Trapezium)}~=~\dfrac{1}{2}~×~(a~+~b)~×~h}}[/tex]

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[tex]\qquad{\sf:\implies{605~=~\dfrac{1}{2}~×~(21~+~x)~×~24.2}}[/tex]

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[tex]\qquad{\sf:\implies{\dfrac{605~×~2}{1}~=~(21~+~x)~×~24.2}}[/tex]

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[tex]\qquad{\sf:\implies{\dfrac{1210}{1}~=~(21~+~x)~×~24.2}}[/tex]

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[tex]\qquad{\sf:\implies{1210~=~(21~+~x)~×~24.2}}[/tex]

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[tex]\qquad{\sf:\implies{1210~×~\dfrac{1}{24.2}~=~21~+~x}}[/tex]

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[tex]\qquad{\sf:\implies{\dfrac{1210~×~1}{24.2}~=~21~+~x}}[/tex]

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[tex]\qquad{\sf:\implies{\cancel\dfrac{1210}{24.2}~=~21~+~x}}[/tex]

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[tex]\qquad{\sf:\implies{50~=~21~+~x}}[/tex]

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[tex]\qquad{\sf:\implies{x~=~50~-~21}}[/tex]

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[tex]\qquad:\implies{\pmb{\underline{\boxed{\pink{\frak{x~=~29cm }}}}}}[/tex]★

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Hence,

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[tex]\qquad[/tex] ∴ The other side of trapezium is 29cm.

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[tex]{\rule{190pt}{2pt}}[/tex]

Step-by-step explanation:

Area of trapazium=1/2×(a+b)×height

605=1/2×24.2(a+21)

605=12.1(a+21)

605=12.1a+254.1

605-254.1/12.1=a

29=a

hope this helps you di