![]() ![]() So, the area of two circles would be πr 2 πr 2 = 2πr 2. The top and bottom, which are circles, are easy to visualize. Ideo: Surface Area of a Rectangular PrismĪ cylinder has a total of three surfaces: a top, bottom, and middle. SA = 2Įxample 2: Given l = 6 mm, w = 9 mm, and h = 8 mm, the surface area would be. Let's calculate the area of each surface.Įxample 1: Given l = 4 yds, w = 2 yds, and h = 5 yds, the surface area would be. Using the labeling of the general prism diagram above, a formula can be created for dealing with the surface area of prisms. The surface are of a prism is nothing more than the sum of all the areas of these rectangles. There is a front, back, top, bottom, left, and right to every rectangular prism. The area of rectangles have been discussed in another section, which is available for review before proceeding, if necessary.Īs the diagram below indicates, there are six surfaces to a rectangular prism. This makes calculating the areas of these surfaces very easy to do. ![]() It is also a figure most people have personal experience due to either wrapping or opening gifts.Īll the surfaces of a prism are rectangular. It is the most simple figure of all the solids. Total Surface Area = Lateral Area Area of Baseįor a cylinder, we can also develop formulas from the net.This is the best figure to begin with when investigating surface area. 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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