https://file.aiquickdraw.com/mathbot/file/1730139460657p76owsls.jpg

The image shows a parallelogram \( ABCD \) with one of its diagonals, \( AC \), and some dimensions labeled:

- Side \( AD = 10 \) units
- Side \( DC = 15 \) units
- Angle \( \angle DAC = 60^\circ \)

The text in Arabic translates to "Calculate the area of the parallelogram."

### Solution

In a parallelogram, the area \( A \) can be calculated using the formula:
\[
A = \text{base} \times \text{height}
\]
or, when we know two adjacent sides and the included angle, we can use the formula:
\[
A = a \times b \times \sin(\theta)
\]
where:
- \( a = AD = 10 \) (one side),
- \( b = DC = 15 \) (adjacent side),
- \( \theta = 60^\circ \) (included angle between \( AD \) and \( DC \)).

Using the formula:
\[
A = 10 \times 15 \times \sin(60^\circ)
\]
Since \( \sin(60^\circ) = \frac{\sqrt{3}}{2} \approx 0.866 \),
\[
A = 10 \times 15 \times 0.866 = 129.9
\]

So, the area of the parallelogram \( ABCD \) is approximately **129.9 square units**.

Would you like further details on the trigonometric calculations, or have any questions?

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### Related Questions
1. How do we calculate the area of a parallelogram given only its diagonals?
2. What is the relationship between the sides and angles in a parallelogram?
3. How can we find the height of a parallelogram given one side and the area?
4. How do we calculate the area if only the side lengths are known, without any angles?
5. How can we determine the perimeter of a parallelogram if all sides are known?

### Tip
In a parallelogram, opposite angles are equal, and opposite sides are both equal and parallel. This can help in solving various geometry problems involving parallelograms.

Calculate the area of a parallelogram ABCD given AD = 10, DC = 15, and ∠DAC = 60°.

Learn how to calculate the area of a parallelogram ABCD with side lengths AD = 10, DC = 15, and included angle ∠DAC = 60°. This solution includes the trigonometric area formula and step-by-step calculations for Grades 9-10.

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