What is the formula for calculating the surface area of a rectangle?

What is the formula for calculating the surface area of a rectangle?

• A. 2lw + 2lh
• B. lw + l + w
• C. lh + 2lw
• D. 2lw + 2wh + 2lh

Answer: (D)

The surface area of a rectangle is typically calculated using the formula that accounts for all the sides of a rectangular prism (rectangular box). The correct formula for the surface area includes each pair of opposite faces of the rectangle. In the context of a rectangular prism, each dimension is represented as length (l), width (w), and height (h). To derive the formula, it is important to consider that a rectangular prism has six faces: two each of length times width, length times height, and width times height. The contribution to surface area from each dimension includes: - 2 times the area of the length and width (2lw), - 2 times the area of the length and height (2lh), - 2 times the area of the width and height (2wh). Therefore, the total surface area is calculated as follows: Surface Area = 2lw + 2lh + 2wh. This elaboration confirms why the chosen formula reflects the accurate computation of the surface area of a rectangular prism by summing the areas of all six sides.

The surface area of a rectangle is typically calculated using the formula that accounts for all the sides of a rectangular prism (rectangular box). The correct formula for the surface area includes each pair of opposite faces of the rectangle. In the context of a rectangular prism, each dimension is represented as length (l), width (w), and height (h).

To derive the formula, it is important to consider that a rectangular prism has six faces: two each of length times width, length times height, and width times height. The contribution to surface area from each dimension includes:

• 2 times the area of the length and width (2lw),

• 2 times the area of the length and height (2lh),

• 2 times the area of the width and height (2wh).

Therefore, the total surface area is calculated as follows:

Surface Area = 2lw + 2lh + 2wh.

This elaboration confirms why the chosen formula reflects the accurate computation of the surface area of a rectangular prism by summing the areas of all six sides.