![]() 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. Volume of a cuboid = length × breadth × height = 12 × 8 × 6 = 576 cm 3.3-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. Ques: What is the volume of a cuboid whose length = 12 cm, breadth = 8 cm, height = 6 cm. Thus, the new surface area of cuboid = 2(4lb + 4bh + 4hl) The surface area of cuboid = 2(lb + bh + hl) Ques: If each edge of a cuboid of surface area S is doubled, then the surface area of the new cuboid will be: (2 marks) (2 marks)Īns: The primary difference between the total surface area (TSA) and curved surface area (CSA) is that the total surface area refers to the area of all the faces of the solid, while, on the other hand, the curved surface area is referred to as the area of the curved region of the solid which excludes the areas of top and bottom regions. Ques: Differentiate between total surface area and curved surface area.
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