To solve for the area of the figure, we need to find the areas of the rectangle and the triangle separately and then sum them.

Step 1: Area of the rectangle

The area $A$ of a rectangle is given by the formula: $A = \text{base} \times \text{height}$

• Base = 18 inches
• Height = 15 inches

So, $A_{\text{rectangle}} = 18 \times 15 = 270 \, \text{in}^2$

Step 2: Area of the triangle

The area $A$ of a triangle is given by: $A = \frac{1}{2} \times \text{base} \times \text{height}$

• Base = 12 inches
• Height = 9 inches

So, $A_{\text{triangle}} = \frac{1}{2} \times 12 \times 9 = 54 \, \text{in}^2$

Step 3: Total area of the figure

To find the total area, add the area of the rectangle and the area of the triangle: $A_{\text{total}} = A_{\text{rectangle}} + A_{\text{triangle}} = 270 + 54 = 324 \, \text{in}^2$

Thus, the area of the figure is 324 square inches.

Would you like further details or have any questions?

Related Questions:

1. How would the area change if the height of the triangle was doubled?
2. How do you calculate the perimeter of this figure?
3. What if the entire shape was a parallelogram, how would the area change?
4. How can we calculate the area of a circle inscribed inside the triangle?
5. How do you find the area of irregular shapes?

Tip: Always label the dimensions carefully and double-check units when calculating areas.