Question

In the given figure ABCD is a trapezium in which AB = 40 m, BC = 15 m, CD = 28 m, AD = 9 m and CE ⊥ AB. The area of trap. ABCD is ______.

Options

• 306 m²

• 316 m²

• 296 m²

• 284 m²

Answer 1

In the given figure ABCD is a trapezium in which AB=40 m, BC =15 m, CD = 28 m, AD = 9 m and CE ⊥ AB. The area of trap. ABCD is 306 m².

Explanation:

Put A = (0, 0), B = (40, 0). 

Let CE ⟂ AB meet AB at E.

So C = (x, h) and D = (x – 28, h).

From AD = 9: (x – 28)² + h² 

= 9²

= 81 

From BC = 15: (40 – x)² + h²

= 15²

= 225

Subtracting the two equations gives x = 28.

So h² = 225 – (40 – 28)²

= 225 – 144

= 81

⇒ h = 9

Area of trapezium = `1/2 xx ("sum of parallel sides") xx "height"`

= `1/2 xx (40 + 28) xx 9`

= 306 m²