https://file.aiquickdraw.com/mathbot/file/172974241053216tgx4gj.jpg

This image shows a parallelogram-shaped figure, with the following dimensions labeled:

- One side is 6 yards
- Another side is 4 yards
- A vertical height of 3 yards
- A diagonal of 5 yards

The angle in the center marked in red indicates that it forms a right angle, suggesting that this is related to calculating the area or possibly verifying relationships involving the height or diagonal.

### To calculate the **area of this parallelogram**, you can use the formula:

\[
\text{Area} = \text{base} \times \text{height}
\]

From the figure:
- The base is 4 yards.
- The height is 3 yards (since the height is perpendicular to the base).

So the area \( A \) is:

\[
A = 4 \, \text{yd} \times 3 \, \text{yd} = 12 \, \text{square yards}
\]

Would you like further details or clarification on any part of this?

### Related Questions:
1. How can we verify if the given sides form a parallelogram?
2. Can the diagonal help calculate other properties of the parallelogram?
3. How would we calculate the perimeter of this parallelogram?
4. Can we use trigonometry to find the angles of this shape?
5. How would the area change if the height were different?

### Tip:
In parallelograms, knowing the height is crucial for calculating the area, not the slant height or diagonals.

How can we calculate the area of a parallelogram with a base of 4 yards, a height of 3 yards, and other dimensions as shown?

Learn how to calculate the area of a parallelogram with a base of 4 yards and a height of 3 yards using the area formula for parallelograms. This problem covers key geometric concepts, including how height is perpendicular to the base and the application of the Pythagorean theorem.

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