https://file.aiquickdraw.com/mathbot/file/17250988714321zs770b0.jpg

To find the area of the kite \(ABCD\) shown in the image, where:

- \(AB = 20 \, \text{cm}\)
- \(AC = 30 \, \text{cm}\) (diagonal)
- \(BD = 24 \, \text{cm}\) (diagonal)

### Understanding the Kite's Properties:
A kite has two pairs of adjacent sides that are equal, and its diagonals intersect at right angles. The area \(A\) of a kite can be calculated using the formula:
\[
A = \frac{1}{2} \times d_1 \times d_2
\]
where \(d_1\) and \(d_2\) are the lengths of the diagonals.

### Given:
- \(d_1 = AC = 30 \, \text{cm}\)
- \(d_2 = BD = 24 \, \text{cm}\)

### Calculation:
Substitute the given values into the area formula:
\[
A = \frac{1}{2} \times 30 \, \text{cm} \times 24 \, \text{cm}
\]
\[
A = \frac{1}{2} \times 720 \, \text{cm}^2
\]
\[
A = 360 \, \text{cm}^2
\]

### Final Answer:
The area of the kite \(ABCD\) is \(360 \, \text{cm}^2\).

Would you like further explanations or have any questions? Here are some related questions you might consider:

1. How does the area formula for a kite compare with that of a rhombus?
2. How do you verify the diagonals intersect at right angles in a kite?
3. What is the relationship between the angles formed by the diagonals in a kite?
4. How can you find the length of one diagonal if the area and the other diagonal are known?
5. How do you differentiate between a kite and a rhombus based on their properties?

**Tip:** Remember that in a kite, one diagonal bisects the other at right angles, which is crucial for calculating the area.

Learn how to find the area of kite ABCD with diagonals AC = 30 cm and BD = 24 cm using the formula A = 0.5 * d1 * d2. This problem explores key geometric concepts, including kite properties and diagonal intersections. Suitable for students in Grades 6-8.

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