Question

The lengths of the shorter and longer parallel sides of a trapezium are x cm and y cm respectively. If the area of the trapezium is (x² – y²), then the height of the trapezium is 

(a) x 

(b) (x + y) 

(c) y 

(d) 2(x – y)

Answer 1

(d) 2(x – y)

Area of trapezium = \(\frac12\)× (Sum of parallel sides) × height 

⇒ \(\frac12\) × (x + y) × height = (x² – y²) 

⇒ height = \(\frac{2(x+y)(x-y)}{(x+y)}\) = 2(x – y)