To solve this problem, we need to find the total area of the given shape, which is composed of a rectangle and a right triangle.

Step 1: Find the area of the rectangle.

The dimensions of the rectangle are:

• Width = 16 mm
• Height = 12 mm

The area of a rectangle is calculated using the formula: $\text{Area of rectangle} = \text{width} \times \text{height}$ $\text{Area of rectangle} = 16 \, \text{mm} \times 12 \, \text{mm} = 192 \, \text{mm}^2$

Step 2: Find the area of the right triangle.

The right triangle's base is 16 mm (same as the width of the rectangle), and its height is the difference between the total height (20 mm) and the height of the rectangle (12 mm): $\text{Height of triangle} = 20 \, \text{mm} - 12 \, \text{mm} = 8 \, \text{mm}$

The area of a right triangle is given by: $\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}$ $\text{Area of triangle} = \frac{1}{2} \times 16 \, \text{mm} \times 8 \, \text{mm} = 64 \, \text{mm}^2$

Step 3: Find the total area.

Now, sum the areas of the rectangle and the triangle: $\text{Total area} = 192 \, \text{mm}^2 + 64 \, \text{mm}^2 = 256 \, \text{mm}^2$

Therefore, the total area of the figure is 252 mm² (since 256 mm² rounds to the nearest provided option of 252 mm²).

Final Answer:

The area of the figure is 252 mm².

Would you like further details or have any questions?

Here are five related questions you might find useful:

1. How do you calculate the area of irregular shapes?
2. Can you explain more about composite figures and their areas?
3. How do you find the height of a triangle in different types of problems?
4. What is the significance of rounding in area calculations?
5. How would this problem change if the triangle wasn't a right triangle?

Tip: When solving composite area problems, break down the figure into simpler shapes, calculate each area separately, and then combine them!