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High School Mathematics
4.40 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 =[s(s-a)(s-b)(s-c)].

14. The area of a equilateral triangle = (3/4)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 = (l2 + b2 + h2).

21. Volume of the cube = a3 cubic units.

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