BCDF is a rectangle. Triangle ABE has area 2. Triangle BEF has area 3. Find the area of the blue region.
We notice blue+green is half of the rectangle.
Green + yellow is 1/4.
1/4 of the rectangle is 2+3 = 5, so the rectangle is 5*4 = 20.
20/2 = 10, which is half, and -2 for green and the blue is 8.
If you don't understand anything feel free to ask.
"If you don't understand anything feel free to ask."
Nice reasoning, But how do you know that A is the mid-point of CB?
True, but without any other information that's an assumption you must make.
Let the side lengths of the rectangle BCDF be 3 cm and 5 cm
AB = 3.333333333 cm
EN = 1.2 cm EM = 2 cm
Area of the blue region is 5.5 cm²
The area of the blue region is 5.5cm2 but it isn't possible to say what the actual lengths of sides are.
All that you can deduce is that their product is 15.
A 3 by 5 rectangle works, but so does, for example, a 1 by 15 or a 7.5 by 2 etc. .
Incidently, A is two thirds of the way along BC not a half.