To solve this problem, let's assume that the longer diagonal of the rhombus is represented by the variable 'd'. According to the problem, the length of one diagonal is 80% of the other diagonal. Therefore, the length of the shorter diagonal can be represented as 0.8d.

We know that the diagonals of a rhombus bisect each other at right angles. Therefore, we can divide the rhombus into four congruent right-angled triangles.

Let's label the length of one side of the rhombus as 'a'. Since the diagonals bisect each other at right angles, the length of the hypotenuse of each right-angled triangle is 'd/2'. Using the Pythagorean theorem, we can find the length of the other two sides of the triangle.

Using the Pythagorean theorem, we have:
a^2 + (0.8d/2)^2 = (d/2)^2

Simplifying the equation, we get:
a^2 + 0.64d^2/4 = d^2/4

Multiplying both sides of the equation by 4 to eliminate the fractions, we have:
4a^2 + 0.64d^2 = d^2

Rearranging the equation, we get:
0.64d^2 - d^2 + 4a^2 = 0

Combining like terms, we have:
-0.36d^2 + 4a^2 = 0

Dividing both sides of the equation by d^2, we get:
-0.36 + 4(a^2/d^2) = 0

Simplifying the equation, we have:
4(a^2/d^2) = 0.36

Taking the square root of both sides of the equation, we have:
2(a/d) = 0.6

Dividing both sides of the equation by 2, we get:
(a/d) = 0.3

Since the area of the rhombus is given by the formula A = (d1*d2)/2, where d1 and d2 are the diagonals, we can substitute the values we know into the formula.

A = (d*(0.8d))/2
A = (0.8d^2)/2
A = 0.4d^2

Therefore, the area of the rhombus is 0.4 times the square of the length of the longer diagonal. This corresponds to option B, which states that the area is 2/5 (or 0.4) times the square of the length of the longer diagonal.