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प्रश्न
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.
उत्तर
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` [∵ Pythagoras theorem]
And in ΔBCF, `CF^2= BC^2 – BF^2` [∵ By Pythagoras theorem]
`⇒25=sqrt(26^2-(17-x)^2)`
`⇒25^2-x^2=25^2-(289-x^2-34-x)` [ ∵`(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`(𝑠𝑢𝑚 𝑜𝑓 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑠𝑖𝑑𝑒𝑠)×ℎ𝑒𝑖𝑔ℎ𝑡=`1/2`(60×77)×24=`1644cm^2`
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