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### High School Mathematics4.40 Important Points in Prism

 1. An object having length width and height is called solid. The side portion of a solid are called lateral surfaces. A solid is a three dimensional object. 2. A prism is polyhedron with two identical ends such that the lines joining the corresponding verticies of the two ends are all parallel. Example: brick, a cube, cuboid. 3. Right Prism: A prism whose bases are perpendicular to the lateral edges and all lateral faces are rectangles is called right prism. 4. A prism is named according to the shape of its base. If the base of a prism is a triangle, then the prism is called triangular prism. 5. Number of lateral surfaces of a right prism = Number sides of the base of the prism. 6. Total number of surfaces of a prism = Number of lateral surfaces + 2. 7. Number of edges of a prism = 3 * Number of sides. 8. Sum of the lengths of edges = Number of sides * height + twice the perimeter of the base. That is S = n*h + 2s. 9. Lateral surface of a prism = Perimeter of the base * height. That is, A = p * h. 10. If 'a' is the side of cube. (i). The lateral surface area of the cube = 4a2. (ii). Area of the base of a cube = a2. (iii). The total surface area of a cube = 6a2. 11. If l is the length, w is the width and h is height of a cuboid. (i). Lateral surface area of the cuboid = 2h(l+w). (ii). The area of the base of cuboid = lw. (iii). The total surface area = 2 (lw + lh + wh). 12. In triangular prism. (i). The lateral surface area = ph. (ii). The area of the base = Area of triangle. 13. If a,b and c respectively are the sides of triangle and 's' is its semi-perimeter then area of the triangle =Ö[s(s-a)(s-b)(s-c)]. 14. The area of a equilateral triangle = (Ö3/4)a2. Where a is the side of the triangle. 15. The area of a right angled triangle = 1/2 * ab, Where a, b are the sides containing right angle. 16. The area of a right angled isosceles triangle = 1/2*a2. 17. The area of rhombus = 1/2 * d1 * d2. Where d1, d are the diagonals of rhombus. 18. Volume of cuboid = l * b * h cubic units. 19. Sum of the edges of a cuboid = 4(l + b + h) units. 20. Diagonal of a cuboid = Ö(l2 + b2 + h2). 21. Volume of the cube = a3 cubic units.