Surface area of pentagonal prism = 5ab + 5bh Surface area of trapezoidal prism = h (b + d) + l (a + b + c + d) Surface area of rectangular prism = 2(lw + wh + lh) Surface area of square prism = 2a 2 + 4ah Surface area of triangular prism = bh + (s 1 + s 2 + b)H Surface Area of Prism = (2 × Base Area) + (Base perimeter × height) Observe the table given below to understand this concept behind the surface area of various prisms: Shape The bases of different types of prisms are different so are the formulas to determine the surface area of the prism. There are seven types of prisms based on the shape of the bases of prisms. The total surface area of a prism = Lateral surface area of prism + area of the two bases = (2 × Base Area) + Lateral surface area = (2 × Base Area) + (Base perimeter × height). The lateral surface area of prism = base perimeter × height The lateral area of a prism is the sum of the areas of all its lateral faces whereas the total surface area of a prism is the sum of its lateral area and area of its bases. There are two types of areas that a prism has - the lateral surface area and the total surface area. Πrl, where r is the radius and l is the slant height of the coneĢπrh, where r is the radius and h is the height of the cylinderĤπr 2, where r is the radius of the sphereĪ prism is a 3D solid object made up of two congruent bases which are polygons and congruent lateral faces which are rectangular in shape. Lateral Surface Area (LSA)/Curved Surface AreaĢh (l + w), where l, w, and h are the length, width, and height of the cuboid Observe the table given below to learn the surface area formulas of different 3D shapes. A sphere is one 3D figure which has only one round surface with no flat base. It does not include the area of the bases. The total surface area considers all the faces of the 3D shape including the flat surfaces and the curved surfaces, while the lateral surface area is calculated to find the area occupied by the curved surface of the shape. In this section, we will learn about the various formulas used to calculate the surface area of different objects. There is a different surface area formula for every geometrical shape, but the idea behind all is to get the total area occupied by all the faces of the objects.
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