In the image provided, we are tasked with finding the area of a triangle. The base and height of the triangle are given as perpendicular to each other. The key measurements are:

• The base: 12 inches
• The height: 9 inches

The formula for the area $A$ of a triangle is:

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

Substituting the values:

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

Let me calculate the area.The area of the triangle is $54 \, \text{in}^2$.

Would you like any further details or clarifications?

Here are 5 related questions for further exploration:

1. How would the area change if the height were doubled but the base remained the same?
2. What is the formula for the area of a triangle when the angle between the base and height is not 90 degrees?
3. How can we find the area of a triangle using its three sides (Heron's formula)?
4. What would be the effect on the area if both the base and height were tripled?
5. How do you find the height if only the area and the base are known?

Tip: Always ensure the base and height are perpendicular to use the standard area formula for triangles.