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Question
In the below figure, compute the area of quadrilateral ABCD.
Solution
Given that
DC = 17cm
AD = 9cm and BC = 8cm
In ΔBCD we have
CD2 = BD 2 + BC2
⇒ (17)2 = BD2 + (8)2
⇒ BD2 = 289 - 64
⇒ BD = 15
In ΔABD, we have
AB2 + AD2 = BD2
⇒ (15)2 = AB2 + (9)2
⇒ AB2 = 225 - 81 = 144
⇒ AB = 12
ar ( quad , ABCD) =ar ( ΔABD) + ar ( Δ BCD)
⇒ ar ( quad , ABCD) = `1/2` ( 12 × 9 ) + `1/2` (8 × 17 ) = 54 + 68
= 112cm2
⇒ ar (quad, , ABCD =`1/2`(12 × 9 ) +`1/2 ( 8 × 15 )`
= 54 + 60cm2
= 114cm2
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