# The diagram shows a trapezium. Show that x^2+20x=400The lengths of the parallel sides of the trapezium are x cm and 20cm. The height of the trapezium is 2x cm. The area is 400cm^2.

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You need to remember the area of trapezium such that:

Area trapezium = Area of rectangle + Area of triangle

You need to consider the dimensions of rectangle such that: one of parallel sides of trapezium x is length of rectangle and height of trapezium 2x represents the width of rectangle.

You need to consider the dimensions of triangle such that: the base of triangle is `(20 - x)` and the height is `2x` .

Area trapezium = `x*2x + (1/2)*(20 - x)*2x`

Factoring out 2x and substituting 400 for area of trapezium yields:

`400 = 2x(x + 10 - x/2) =gt 400 = x + 20x^2`

**Hence, the last line proves the identity `400 = x + 20x^2` under the given conditions.**

The area for a trapezium (trapezoid in America) is A=h/2(b1 + b2).

Plug in the values we know:

400 = 2x/2 (20 + x)

Simplify

400 = x(20 + x)

400=20x + x^2