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What is the lateral area of a regular quadrangular prism that has a perimeter of 16 cm and a height of 4 cm?

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March 15, 2007 8:17PM

What makes this question tricky to answer is the understanding of the terms. Were the correct terms used in the question, and does the question poster and answer contributor have the same understanding of those terms? Having said that, here goes. A prism is a polyhedron with at least two congruent parallel faces. They are called the bases. The other faces (the "lateral faces") are parallelograms that are formed by lines that connect the corresponding vertices of the two bases. A quadrangular prism has a quadrangular base (such as a rectangle). If the base is some sort of regular polygon, it's called a regular prism. The lateral area of a prism is defined as the total area of the lateral faces. To calculate the lateral area, you multiply the length of an edge by the perimeter of the face that is perpendicular (at right angles to) to that edge. So, assuming the height, 4 cm in this case, is perpendicular to the perimeter, 16 cm, we calculate the lateral area to be 4 x 16 or 64 square centimeters or 64 cm2.