Assessment and Learning in Knowledge Spaces (ALEKS) Basic Math Placement Practice Test

How is the surface area of a rectangular prism calculated?

1. V = lwh

2. SA = 2(lw + lh + wh)

3. P = side + side + side

4. A = pi x r^2

The correct answer is: SA = 2(lw + lh + wh)

The surface area of a rectangular prism is calculated using the formula SA = 2(lw + lh + wh). This formula takes into account all six faces of the prism by first calculating the area of the three distinct pairs of opposite faces: - The area of the top and bottom faces, which are both rectangles of dimensions length (l) and width (w). - The area of the front and back faces, which are rectangles of dimensions length (l) and height (h). - The area of the left and right faces, which are rectangles of dimensions width (w) and height (h). By determining the area of these three sets of faces and then multiplying by 2 (since there are two of each type of face), the total surface area of the prism is obtained. This method ensures that all sides of the prism contribute to the total surface area, providing an accurate measurement for the entire exterior of the shape. The other choices represent different mathematical concepts and are not applicable to the calculation of a rectangular prism's surface area. The volume formula (A) pertains to the space inside the prism rather than its surface. The perimeter formula (C) would be relevant in a different context, such as calculating the distance around a shape