Lastly, the sides of each rectangle are called edges (again divided into base edges and lateral edges). The bottom and top faces of the box are called bases, and each of the other four is called a lateral face. Note that this, in particular, means that there are three pairs of identical faces placed on opposite sides of the solid.Īlso, as with any other scientific definition, there are a few fancy names associated with the prism. Well, that is a rectangular prism! Or do you remember those drawings of houses that we did in kindergarten? Remove the angular roof, and you're left with another example of a rectangular prism.įormally (mathematically), a right rectangular prism is a solid where all six sides are rectangles that are perpendicular to one another. A regular, rectangular box, just like the ones you see in the supermarket, full of whatever products. Total Surface Area = Lateral Area Area of Baseįor a cylinder, we can also develop formulas from the net.Before we see what the surface area of a rectangular prism is, we should get familiar with the prism itself. To find the total surface area, add the area of the base, B, to the lateral area. Lateral Area = 1 2 \frac × Perimeter of Base × Slant Height of Pyramid The area of the 4 lateral faces is found by adding the widths of all of the individual faces, the perimeter ( P) of the base of the pyramid, and then multiplying by the height of the triangle, which is the slant height, l, of the pyramid. Total Surface Area = Lateral Area 2 × Area of Base To find the total surface area, add the area of the large rectangle plus two times the area of the base, B. Next, find the area of one of the two congruent bases, area B. Lateral Area = Perimeter of Base × Height of Prism The area of the big rectangle is found by adding the widths of all of the individual faces, the perimeter ( P) of the prism, and then multiplying by the height. The diagram shows the lateral faces of the prism forming one big rectangle. We know that the area of a rectangle is the product of the length and the width, so if we label the dimensions of each of the faces of the prism, we can calculate the surface area of the prism. The bases of the prism are highlighted in blue. Now that you have explored nets of 3-dimensional figures, let's use those nets to generate formulas for surface areas of prisms, pyramids, and cylinders.įirst, consider the net below for a rectangular prism. The barn is a prism with a seven-sided polygon as the base, so we can call the barn a heptagonal prism. The silo is in the shape of a cylinder with a half-dome roof. Since the surfaces of a cylinder are not polygons (they have round edges and are not always planar figures), we call them surfaces instead of faces.Ĭonsider the barn and silo shown. A cylinder has two circular bases and a curved lateral surface. A pyramid with a square base is called a square pyramid.Ī cylinder is like a prism, but the bases of a cylinder are circles instead of polygons. Like prisms, pyramids are named by the shape of their base. The lateral faces of a pyramid are triangles that meet at one point, which is called the vertex. Likewise, a prism with a hexagonal-shaped base is called a hexagonal prism.Ī pyramid is a 3-dimensional figure that has one base. So, a prism with a rectangular-shaped base is called a rectangular prism. A prism is named by the shape of its base. The lateral faces of a prism are always parallelograms and are usually rectangles. 3-dimensional figures occur everywhere in the world around us, especially in fields such as architecture.Ī prism is a 3-dimensional figure that has two parallel, congruent bases connected by lateral faces.
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