BCDF is a rectangle. Triangle ABE has area 2. Triangle BEF has area 3. Find the area of the blue region.

Guest May 12, 2020

#1**+1 **

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.

hugomimihu May 12, 2020

#2**+1 **

*"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?

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Guest May 12, 2020

#5**+1 **

True, but without any other information that's an assumption you must make.

hugomimihu
May 12, 2020

#3**+1 **

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 **

Dragan May 12, 2020

#6**0 **

The area of the blue region is 5.5cm^{2} 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.

Guest May 12, 2020