Mathematics ACT Aspire Practice Test

What is the first step in finding the surface area of a triangular prism?

1. Calculate the perimeter

2. Find the area of the triangle base

3. Add the lengths of all faces

4. Multiply the base and height of the triangle

The correct answer is: Find the area of the triangle base

To find the surface area of a triangular prism, the first step involves determining the area of the triangle base. This is critical because the surface area calculation starts from the base, which affects the dimensions of the entire prism. The surface area of a triangular prism consists of two triangular bases and three rectangular lateral faces. Therefore, knowing the area of the triangle allows you to calculate the total contribution of the two bases to the surface area. Once the area of the triangular base is calculated, you can then proceed to measure and sum up the areas of the adjacent rectangular faces and add them all together to get the total surface area. Calculating the perimeter would be relevant later when determining dimensions related to the rectangular faces, but it isn't the first step. Adding the lengths of all faces would come after calculating the areas. Multiplying the base and height of the triangle alone is part of finding the area, but the correct first step is to gather all necessary dimensions to accurately calculate this area. Thus, the focus should initially be on finding the area of the triangle base before moving on to other steps in the process.