Question

In the below figure, compute the area of quadrilateral ABCD.

Answer 1

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