https://file.aiquickdraw.com/mathbot/file/17298970426143btkwr73.jpg

To calculate the area of the largest right triangle in the image, let's analyze the information provided:

1. The triangle is a right triangle.
2. The two legs of the triangle are given as:
   - One leg is 9 cm.
   - The other leg is 4 cm.

### Area of a Right Triangle
For a right triangle with legs of length \(a\) and \(b\), the area \(A\) is calculated using the formula:
\[
A = \frac{1}{2} \times a \times b
\]

### Substituting Values
Here, \(a = 9 \, \text{cm}\) and \(b = 4 \, \text{cm}\).
\[
A = \frac{1}{2} \times 9 \times 4
\]
\[
A = \frac{1}{2} \times 36
\]
\[
A = 18 \, \text{cm}^2
\]

### Final Answer
The area of the largest right triangle is:
\[
18 \, \text{cm}^2
\]

Would you like more details on the solution process or have any questions?

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Here are some related questions for further exploration:
1. What is the perimeter of this right triangle?
2. How do you calculate the hypotenuse of a right triangle with given legs?
3. Can the Pythagorean theorem be used to find other triangle properties here?
4. How does changing the length of one leg affect the area?
5. What is the area formula for non-right triangles?

**Tip:** In a right triangle, the area formula is simplified as it depends solely on the lengths of the two legs.

Calculate the area of the largest right triangle in the picture below: (One leg is 9 cm and the other leg is 4 cm)

Learn how to calculate the area of a right triangle with legs measuring 9 cm and 4 cm. This geometry problem demonstrates how to apply the area formula for right triangles, suitable for students in Grades 6-8.

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