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?

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.