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Question
In a trapezium ABCD, it is given that AB║CD and AB = 2CD. Its diagonals AC and BD intersect at the point O such that ar(ΔAOB) = 84cm2. Find ar(ΔCOD).
Solution
In Δ AOB and COD
∠𝐴𝐵𝑂= ∠𝐶𝐷𝑂 (𝐴𝑙𝑡𝑒𝑟𝑛𝑡𝑒 𝑎𝑛𝑔𝑙𝑒𝑠 𝑖𝑛 𝐴𝐵∥𝐶𝐷)
∠𝐴𝑂𝐵= ∠𝐶𝑂𝐷 (𝑉𝑒𝑟𝑡𝑖𝑐𝑎𝑙𝑙𝑦 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑎𝑛𝑔𝑙𝑒𝑠)
By AA similarity criterion, ΔAOB ~ ΔCOD
If two triangles are similar, then the ratio of their areas is equal to the ratio of the squares of their corresponding sides.
∴ `(area (Δ AOB))/(area(Δ COD))=((AB)/(CD))^2`
⇒ `84/(area(ΔCOD))=((2CD)/(CD))^2`
⇒` area (Δ COD)=12 cm^2`
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