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Question
Find the area of the trapezium ABCD in which AB || DC, AB = 18 cm, ∠B = ∠C = 90°, CD = 12 cm and AD = 10 cm.
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Solution
In trapezium ABCD,
AB || DC, AB = 18 cm
∠B = ∠C = 90°, CD = 12 cm and AD = 10 cm.
Area of trapezium ABCD
Draw DL ⊥ AB
∴ AL = 18 - 12 = 6 cm
DL = BC
DL = `sqrt("AD"^2 - "AL"^2)`
= `sqrt(10^2 - 6^2) = sqrt(100 - 36)`
= `sqrt(64) = 8 "cm"`
Now area of trapezium = `1/2 ("AB + CD") xx "DL"`
= `1/2(18 + 12) xx 8 "cm"^2`
= `1/2 xx 30 xx 8 = 120 "cm"^2`
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