See the table 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 we read above based on the shape of the bases. The total surface area of a prism = Lateral surface area of prism + area of the two bases = (2 × Base Area) + Lateral surface area or (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 we read about, first, the lateral surface area of the prism, and second, the total surface area of the prism. Let us learn these two in the case of prisms. The two formulas are the area of the shape and volume of the shape. There are two basic formulas we read in geometry about all the respective 3-dimensional shapes. Trapezoidal Prism: A prism whose bases are trapezoid in shape is considered a trapezoidal prism.Octagonal Prism: A prism whose bases are octagon in shape is considered an octagonal prism.Hexagonal Prisms: A prism whose bases are hexagon in shape is considered a hexagonal prism.Pentagonal Prism: A prism whose bases are pentagon in shape is considered a pentagonal prism.Rectangular prism: A prism whose bases are rectangle in shape is considered a rectangular prism (a rectangular prism is cuboidal in shape).Square Prism: A prism whose bases are square in shape is considered a square prism.Triangular Prism: A prism whose bases are triangle in shape is considered a triangular prism.Oblique Prism: An oblique prism appears to be tilted and the two flat ends are not aligned and the side faces are parallelograms.Ī prism is named on the basis of the shape obtained by the cross-section of the prism. Right Prism: A right prism has two flat ends that are perfectly aligned with all the side faces in the shape of rectangles.There are two different prisms based on the alignment of the bases named: Prisms Based on the Alignment of the Identical Bases. Irregular Prism: If the base of the prism is in the shape of an irregular polygon, the prism is an irregular prism.Regular Prism: If the base of the prism is in the shape of a regular polygon, the prism is a regular prism.There are two types of prisms in this category named as: Prisms can be classified on the following basis: Prisms Based on the Type of Polygon, of the BaseĪ prism is classified on the basis of the type of polygon base it has. S 1 and S 2 are the three sides of the base triangleĪlso Read: Angle Sum Property of QuadrilateralĪ right triangular prism with equilateral bases and square sides is called a uniform triangular prism.Before reading about various types of prisms let us understand on what basis types of prisms can be obtained. Thus, adding all the areas, the total surface area of a right triangular prism is given by, Lateral surface area is the product of the length of the prism and the perimeter of the base triangle = (S 1 + S 2 + h) × l. Lateral Surface Area = (S 1 + S 2 + S 3 ) × LĪ right triangular prism has two parallel and congruent triangular faces and three rectangular faces that are perpendicular to the triangular faces.Īrea of the two base triangles = 2 × (1/2 × base of the triangle × height of the triangle) which simplifies to 'base × height' (bh). Thus, the lateral surface area of a triangular prism is: It is the sum of all the areas of the vertical faces. Lateral Surface area is the surface area of the prism without the triangular base areas. S 1, S 2, and S 3 are the three sides of the base triangle Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)ī is the resting side of the base triangle, Thus, the formula for the surface area of a triangular prism is: The area of the two triangular bases is equal to The sum of areas of the parallelograms joining the triangular base is equal to the product of the perimeter of the base and length of the prism. The surface area of a triangular prism is obtained by adding all the surface areas of faces that constitute the prism. Derivation of Surface Area of Triangular Prism
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