The problem states that BD is a diagonal of a rectangle and it divides the rectangle into two equal parts. We need to find the area of triangle ABD.

1. Problem Description

The problem states that BD is a diagonal of a rectangle and it divides the rectangle into two equal parts. We need to find the area of triangle ABD.

2. Solution Steps

Let the area of the rectangle be $A_{rectangle}$.

Since the diagonal BD divides the rectangle into two equal parts, the area of triangle ABD is half the area of the rectangle. Therefore:

$A_{ABD} = \frac{1}{2} A_{rectangle}$

Since we are not given the dimensions of the rectangle, we cannot find a numerical value for the area of triangle ABD. However, we can express the area of triangle ABD in terms of the area of the rectangle. If the sides of the rectangle are $l$ and $w$, then $A_{rectangle} = l \times w$. Therefore, $A_{ABD} = \frac{1}{2} l \times w$.

Since the question only asks for the area of triangle ABD in relation to the rectangle and does not provide dimensions, it is sufficient to say it's half the area of the rectangle.

3. Final Answer

The area of triangle ABD is half the area of the rectangle.