To solve the problem of finding the area of the given figure, we can break it into two separate parts:

1. The rectangle on the right-hand side.
2. The right triangle on the left-hand side.

Step 1: Calculate the area of the rectangle

The dimensions of the rectangle are:

• Width: 12 inches
• Height: 17 inches

The area of a rectangle is given by: $\text{Area of rectangle} = \text{Width} \times \text{Height}$ $\text{Area of rectangle} = 12 \, \text{in} \times 17 \, \text{in} = 204 \, \text{square inches}$

Step 2: Calculate the area of the right triangle

The dimensions of the right triangle are:

• Base: 16 inches (this is the bottom horizontal distance).
• Height: 11 inches (the vertical height from the base to the top of the triangle).

The area of a right triangle is given by: $\text{Area of triangle} = \frac{1}{2} \times \text{Base} \times \text{Height}$ $\text{Area of triangle} = \frac{1}{2} \times 16 \, \text{in} \times 11 \, \text{in} = 88 \, \text{square inches}$

Step 3: Add the two areas together

The total area of the figure is the sum of the areas of the rectangle and the triangle: $\text{Total Area} = \text{Area of rectangle} + \text{Area of triangle}$ $\text{Total Area} = 204 \, \text{in}^2 + 88 \, \text{in}^2 = 292 \, \text{square inches}$

Final Answer:

The total area of the given figure is: $\boxed{292 \, \text{square inches}}$

Would you like further clarification or a detailed breakdown of any step? Here are some related questions you can explore:

1. How do you calculate the area of irregular shapes by dividing them into simpler parts?
2. What is the formula for the area of a trapezoid, and how does it differ from this case?
3. Could this problem be solved differently (e.g., by subtracting areas instead of adding)?
4. How would the calculation change if the triangle was not a right triangle?
5. Can you use this process to calculate volumes of three-dimensional shapes?

Tip:

Always label dimensions clearly in complex figures to avoid confusion when identifying shapes and their sizes.