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Question
Two parallel side of a trapezium are 60 cm and 77 cm and other sides are 25 cm and 26 cm. Find the area of the trapezium.
Solution
Given that two parallel sides of trapezium are AB = 77 and CD = 60 cm
Other sides are BC = 26 m and AD = 25 cm.
Join AE and CF
Now, DE ⊥ AB and CF ⊥ AB
∴ DC = EF = 60 cm
Let AE = x
⇒ BF = 77 – 60 – x = 17 – x
`In ΔADE, DE^2 = AD^2 – AE^2 = 25^2 – x^2` [โต Pythagoras theorem]
And in ΔBCF, `CF^2= BC^2 – BF^2` [โต By Pythagoras theorem]
`⇒25=sqrt(26^2-(17-x)^2)`
`⇒25^2-x^2=25^2-(289-x^2-34-x)` [ โต`(a-b)^2=a^2-2ab+b^2` ]
`⇒265-x^2=676-289-x^2+34x`
`34x=238`
`x=7`
`∴ DE =sqrt(25^2-x^2)=sqrt(625-7^2)=sqrt(516)=24cm`
∴ Area of trapezium = `1/2`(๐ ๐ข๐ ๐๐ ๐๐๐๐๐๐๐๐ ๐ ๐๐๐๐ )×โ๐๐๐โ๐ก=`1/2`(60×77)×24=`1644cm^2`
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