The area of a triangle is a quarter of that of a square;

The key is to prove that the area of small triangle BME is a quarter of that of middle triangle BCM (the area ratio is the square of the corresponding edge ratio).

Then, the BCM area of the middle triangle is four-fifths of the CEB area of the big triangle.

The result is (4/5) * (1/4) = 4/20 =1:5.