Mathematics ACT Aspire Practice Test

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Study for the Mathematics ACT Aspire Test. Master concepts through a mix of questions. Dive into explanations and hints for a thorough understanding. Elevate your test readiness!

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In a triangular prism, how do you calculate the total surface area?

By only adding triangular face areas
By adding triangular and rectangular face areas
By using only rectangular areas
By calculating the height alone

The correct answer is: By adding triangular and rectangular face areas

To find the total surface area of a triangular prism, you must consider the areas of all the faces that make up the prism. A triangular prism has two triangular faces and three rectangular faces. By calculating the area of the two triangular bases, you ensure that both ends of the prism are accounted for. In addition, you need to include the areas of the three rectangles that connect the corresponding sides of the triangular bases. The process involves measuring the dimensions of the triangular bases and the lengths of the sides and then using the appropriate formulas: the area of a triangle (which is typically 1/2 * base * height for the triangular faces) and the area of rectangles (length * width). Thus, adding together the areas of both the triangular faces and the three rectangular faces gives the total surface area of the prism. Focusing solely on triangular or rectangular areas separately would not provide a complete calculation of the surface area. Additionally, considering only the height of the prism does not offer any information regarding the dimensions necessary for surface area calculations.