Volume of a pyramid = 1/3 * area of base * slant height

Ex: find the surface area and volume of a pyramid whose base is an equilateral triangle of sides 5cm and whose height is 20cm

Solution:

                       5cm                     h

                              2.5cm

                         h = 52-2.52 = 18.75 = 4.3

                        Area of pyramid = area of slant triangle * area of base

Area of slant triangle = perimeter of base * slant height = (2.5 * 3) * 20 = 7.5 * 20 = 150cm²

Volume of pyramid = 1/3 * area of base * slant height = 1/3 * (1/2 * 5 * 4.3) * 20 = 1/3 * 10.75 * 20 = 71.67cm³