The problem in the uploaded image appears to involve finding areas of certain shapes related to a parallelogram $ABCD$. Here’s a step-by-step explanation of the problem and its solution:

Problem Overview:

1. $ABCD$ is a parallelogram.
2. It is mentioned that certain sub-areas (e.g., triangles within the parallelogram) have equal areas, and the relationships among their areas are given.
3. The problem requires determining the relationship between these areas.

Explanation:

Given in the image:

• The area of $\triangle ABD = \triangle BCD$, because diagonals of a parallelogram divide it into equal areas.
• Hence, $\text{Area of } \triangle ABCD = 2 \cdot \text{Area of } \triangle ABD$.
• Also, from the problem: $\text{Area of } \triangle ABD = \text{Area of } \triangle BCD$.

From these relationships:

• The diagonals divide the parallelogram into four triangles of equal area: $\text{Area of each triangle} = \frac{1}{2} \times \text{Area of } ABCD.$

Final Answer:

• If the total area of parallelogram $ABCD$ is $A$, then the area of each triangle formed by its diagonals is: $\frac{1}{4} \times A.$

Would you like further clarification or assistance with related questions? Here are 5 related questions to expand on this topic:

1. How can you derive the area of a parallelogram using base and height?
2. Why do the diagonals of a parallelogram divide it into four triangles of equal area?
3. How is the area of a triangle calculated using vectors if its vertices are given?
4. What are the properties of the diagonals of a parallelogram related to its area?
5. How does the area calculation change if $ABCD$ is a rectangle instead of a general parallelogram?

Tip: Always use symmetry and basic properties of geometrical shapes like parallelograms to simplify area calculations.