https://file.aiquickdraw.com/mathbot/file/1726914519607mvhivyfl.jpg

The triangle \( \triangle ABC \) in the image appears to be a right triangle, with a right angle at \( D \). To find the area of \( \triangle ABC \), we can use the formula for the area of a triangle:

\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

From the diagram, we have:
- Base \( AB \) can be calculated using the Pythagorean theorem, since \( AD = 5 \) cm and \( CD = 10 \) cm.
- Height \( CD = 10 \) cm.

Let's calculate \( AB \), and then the area of the triangle.The length of side \( AB \) is approximately \( 11.18 \, \text{cm} \), and the area of \( \triangle ABC \) is approximately \( 55.90 \, \text{cm}^2 \).

Would you like more details or have further questions?

Here are 5 related questions to explore:
1. How do we apply the Pythagorean theorem in various triangle types?
2. What other methods can be used to find the area of non-right triangles?
3. How can we find the area if only the sides of a triangle are known?
4. What is the significance of congruence in triangles?
5. How does similarity differ from congruence in geometry?

**Tip:** For triangles, always check if they are right triangles to simplify calculations using the Pythagorean theorem.

Discover how to calculate the area of Triangle ABC using geometry principles and the Pythagorean theorem. Learn about the triangle's properties, such as its right angle at point D, and find the area with the dimensions given in the problem. This guide is suitable for students in Grades 7-9.

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