Can two bisectors of a triangle split it into four parts of equal area?

To solve this problem for us, we need to perform the following actions:

If the bisectors are divided into four equal parts, then one divides into two equal parts.
Then the bisector is the median.
Then the triangle is regular.
But in a regular triangle, the bisectors do not divide it into 4 equal parts because there is one more angle that is not divided.

As a result of the actions taken, we get the answer to the problem: no, they cannot.