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...

## See

This Answer NowStart your **48-hour free trial** to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Already a member? Log in here.

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.**