![]() ![]() ![]() ![]() The lateral surface of a cuboid is the sum of the area of the rectangular faces excluding the top and bottom face Note: The cuboid’s total surface area is not the same as the lateral surface area of a cuboid. The total surface area of a cuboid is equal to the sum of the face areas Area of the two side faces = wh+ wh = 2wh.Area of the front and back face = lh+ lh = 2lh.Area of the top and bottom face = lw+ lw = 2lw.To find the surface area of a cuboid, you need to calculate the area of each rectangular face and then sum up all the areas to get the total surface area i.e. How to Find the Surface Area of a Cuboid? In this article, we will learn how to find the surface area using a cuboid formula’s surface area. The surface area of a cuboid is the sum of the area of the 6 rectangular faces that cover it. The height (h) of a cuboid is the vertical side. In a cuboid, the horizontal longer side is the length (l), and the shorter horizontal side is the width (w) or breadth (b). Ultimately, a cuboid has the shape of a rectangular prism or a box. In geometry, a cuboid is a 3-dimensional figure with a length, width, and height. For example, a brick, a matchbox, a chalk box, etc., are all cuboids. A cuboid is one of the most common shapes in the environment around us. Total Surface Area = Lateral Area + Area of Baseįor a cylinder, we can also develop formulas from the net.Surface Area of a Cuboid – Explanation & Examplesīefore we get started, let’s discuss what a cuboid is. 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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