Question

In the given figure ABCD is trapezium in which the parallel sides AB and CD both are perpendicular to BC. If AB = 16 m, CD = 8 m and AD = 17 m. What is the area of the trapezium ?

(a) 140 m² 

(b) 168 m² 

(c) 180 m² 

(d) 156.4 m² 

Answer 1

(c) 180 m²

AE = AB – EB = AB – DC = 16 m – 8 m = 8 m 

∴ In Δ AED,

DE² = AD² – AE² = 17² – 8² = 289 – 64 = 225 

⇒ DE = 15 m 

∴ Area of the trapezium ABCD

= \(\frac12\) x (AB + DC) x DE

= \(\frac12\) x (16 m + 8 m) x 15 m

= \(\frac12\) 24 m x 15 m = 180 m².