The image shows a triangle $\triangle XYZ$ with a perpendicular from point $X$ to point $YZ$. Here is a breakdown of the triangle:

1. $XY = 9$ units
2. $XZ = 9$ units
3. $YZ = 3$ units
4. The line $XY$ is perpendicular to $YZ$, making $YZ$ the base and $XY$ the height.

To find the area of $\triangle XYZ$:

The formula for the area of a triangle is:

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

In this case:

• The base $YZ = 3$ units
• The height $XY = 9$ units

Substituting the values:

$\text{Area} = \frac{1}{2} \times 3 \times 9 = \frac{1}{2} \times 27 = 13.5 \text{ square units}$

Thus, the area of $\triangle XYZ$ is 13.5 square units.

Would you like more details or have any further questions?

Here are five related questions to consider:

1. How do we find the height of a triangle when it is not given directly?
2. What properties does an isosceles triangle have, and how do they apply here?
3. How would the area change if $YZ$ was a different length?
4. Can you derive the formula for the area of a triangle using geometry principles?
5. How do perpendicular bisectors help in finding triangle properties?

Tip: Always double-check that you have identified the correct base and height when calculating the area of a triangle.