To find the area of the triangle in the given image, we use the formula for the area of a triangle:

$A = \frac{1}{2} \times \text{base} \times \text{height}$

Step 1: Identify the base and height

From the image:

• The base of the triangle is 9 inches.
• The height of the triangle is 12 inches (as these two are perpendicular).

Step 2: Calculate the area

$A = \frac{1}{2} \times 9 \, \text{in} \times 12 \, \text{in}$

$A = \frac{1}{2} \times 108 \, \text{in}^2$

$A = 54 \, \text{in}^2$

Final Answer:

The area of the triangle is 54 square inches (in²).

Would you like additional details or have any further questions?

Related Questions:

1. How do we find the height in triangles that are not right triangles?
2. What if the base and height are in different units, such as feet and inches?
3. Can you explain how to calculate the area if the triangle's dimensions were scaled up by 2x?
4. How does the concept of area differ for triangles compared to other polygons?
5. Can we use trigonometry to find the area of a triangle?

Tip:

Always ensure the base and height are perpendicular when using this formula for a triangle's area!