Which of the following formulas accurately calculates the area of a shape composed of a rectangle and a triangle?

The formula that accurately calculates the area of a shape that consists of both a rectangle and a triangle is represented by the correct choice.

To understand why this is the case, consider the components of the formula. The first part, (4 \times 9), calculates the area of the rectangle. Here, 4 represents the base and 9 represents the height of the rectangle. The second part, (1/2 \times (4 \times 2)), is used to calculate the area of the triangle. In this context, 4 again represents the base of the triangle, and 2 is the height.

The area of a triangle is determined by the formula ( \frac{1}{2} \times \text{base} \times \text{height} ). Therefore, combining the area of the rectangle with that of the triangle gives a comprehensive calculation for the overall area of the composite shape.

This understanding is what makes this formula a correct choice for finding the total area of a configuration that includes both a rectangle and a triangle. Each component's area is calculated correctly and summed to provide the total area of the entire shape.