The area of triangle $PQR$ can be calculated using the formula for the area of a triangle:

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

From the diagram, we see the following coordinates:

• $P(18,12)$
• $Q(18,0)$
• $R$ lies on the x-axis (though the exact location of $R$ is not directly labeled, it's clear that $R$ aligns with point $Q$).

Step-by-step calculation:

1. Base of triangle $PQR$: The base is the distance between points $Q(18,0)$ and $R(6,0)$. The base is the horizontal distance, i.e., $PQ = |18 - 0| = 18$.

2. Height of triangle $PQR$: The height is the vertical distance from point $P(18,12)$ down to the x-axis (since $Q$ lies on the x-axis). The height is $12$, which is the y-coordinate of point $P$.

3. Area of triangle $PQR$: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 18 \times 12 = \frac{1}{2} \times 216 = 108$

Thus, the area of triangle $PQR$ is $\boxed{108}$ square units.

Let me know if you'd like more details or have any questions! Here are 5 related questions to expand on this:

1. How do we find the coordinates of point $T$ if needed?
2. What is the distance between points $A$ and $P$?
3. How would the area change if the height from point $P$ were doubled?
4. Can you derive the equation of the line passing through points $P$ and $Q$?
5. How would you calculate the perimeter of triangle $PQR$?

Tip: For geometric problems, breaking down coordinates and calculating distances systematically is key to solving for areas and perimeters effectively.