A pyramid is a 3-dimensional geometric figure which consists of 4 triangles along with a base at the bottom. The base of a pyramid can be in different forms like a square or a rectangle. This base of the pyramid is joined by the 4 triangles connecting it to the top most point of the pyramid known as the ‘apex’ or the ‘vertex’ of the pyramid. The total surface area of a pyramid is the sum of the areas of each surface and hence can be calculated accordingly.
Example 1: What is the surface area of a rectangular pyramid which has a base length of 7m, base width of 5m and a slant height of 10m?
Given: base length, l= 7m, base width, w= 5m
Slant height, s= 10m
The base of a rectangular pyramid is a rectangle.
Surface area of the rectangular pyramid= (l* w) + (l* s) + (w* s)
This gives: Surface area of the rectangular pyramid, SA= (7* 5) + (7* 10) + (5* 10) = 155m2
Therefore, the surface area of the given rectangular pyramid is 155m2
Example 2: What is the surface area of a square pyramid which has a base length of 6m and a slant height of 9m?
Given: base length, b= 6m
Slant height of the pyramid, s = 9m
The base of a square pyramid is a square.
Surface area of a square pyramid = b2 + 2* b* s
This gives: Surface area of the square pyramid, SA= (6)2 + (2 * 6 * 9) = 36+ 108= 144m2
Therefore, the surface area of the given square pyramid is 144m2