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)
400 = x(20 + x)
400=20x + x^2