![]() Thus, the lateral surface area of an isosceles triangular prism is LSA = 2la + lb. Therefore, the total area of the three rectangles = 2la + lb Thus, the area of the third rectangle = l × b Let the length of the third rectangle is "l" units and the breadth of the third rectangle = 'b' units Thus, the area of the two congruent rectangles = 2 × l × a ![]() Let the length of the congruent rectangles is "l" units and the breadth of the congruent rectangles is "a" units. So let's first find the area of the 2 congruent rectangles: Since we already know that in an isosceles triangular prism, there are 2 congruent rectangles. ⇒ Area of two isosceles triangles = 2 × 1/2 × b × h = b × h ![]() Let us consider an isosceles triangle with the equal sides be "a" units, the base of each of the triangle be "b" units and the height of the triangle is "h"Īrea of an isosceles triangle = (1/2 × base × height) = 1/2 × b × h The surface area of the isosceles triangular prism is found as SA = Sum of areas of 2 isosceles triangles at the bases + Sum of the areas of the 3 rectangles. The lateral area of an isosceles triangular prism is found as Lateral area, LA = Sum of the areas of all the vertical faces = Sum of the areas of the three rectanglesĭerivation of Surface Area of Isosceles Triangular Prism Since we know that the vertical faces in the case of an isosceles triangular prism are rectangles, therefore, to find the lateral area we will have to find the areas of all the vertical faces and then add them up. Lateral Area refers to the total area of the lateral or vertical faces of any solid. ⇒ SA = Sum of areas of 2 isosceles triangles + Sum of the areas of the 3 rectangles The surface area of an isosceles triangular prism is found as SA = Sum of areas of all the faces To find the surface area of an isosceles triangular prism, we will have to add the areas of the 2 isosceles triangles at the base facing each other and the area of the rectangles formed by the corresponding sides of the two congruent triangles. The surface area of an isosceles triangular prism refers to the sum total of the area of all the faces of an isosceles triangular prism. Find lateral surface area and total surface area.Formula for Surface Area of Isosceles Triangular Prism The base of a triangular prism is ΔABC, where AB = 6 cm, BC = 8 cm and ∠B = 90. Q 1: What will be the surface area of a triangular prism if the apothem length, base length, and height are 5 cm, 10 cm, and 18 cm respectively? 1] Rectangular PrismĪ Rectangular Prism has 2 parallel rectangular bases and 4 rectangular faces.Ī triangular prism has 3 rectangular faces and 2 parallel triangular bases.Ī pentagonal prism has 5 rectangular faces and 2 parallel pentagonal bases.Ī hexagonal prism has six rectangular faces and two parallel hexagonal bases. Prisms are of different types, which are named according to their base shape. The height of the prism is the common edge of two adjacent side faces.With every lateral face, one edge in common with the base and also with the top.Each face is a parallelogram except base and top.The base and top are parallel and congruent.The volume of a prism =Base Area× Height.The surface area of a prism = (2×BaseArea) +Lateral Surface Area.In some cases, it may be a parallelogram. The Prism Formula is as follows, The lateral faces are mostly rectangular. ![]() Lateral faces join the two polygonal bases. In physics (optics), a prism is defined as the transparent optical element with flat polished surfaces that refract light. In mathematics, a prism is a polyhedron with two polygonal bases parallel to each other. Let us now study about prism formula in detail. We can use the concept of prism in both mathematics and science as well. A prism is a solid bounded by a number of plane faces its two faces, called the ends, are congruent parallel plane polygons and other faces, called the side faces, are parallelograms.
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