# Surface Area of a Pyramid

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A pyramid is a 3-dimensional geometric figure which has 4 triangles joining towards a single point known as the ‘apex’ or the ‘vertex’ of the pyramid. There are different types of pyramids depending on the type of base a pyramid has. For instance, a pyramid with a square base is known as square pyramid, a pyramid with a rectangular base is known as a rectangular pyramid etc. Total surface area of a pyramid can be calculated by adding all the areas of every face of the pyramid.

Example 1: What is the surface area of a square pyramid which has a base length of 3m and a slant height of 5m?

Given: base length, b= 3m

Slant height of the pyramid, s = 5m

Since it is a square pyramid, the base of the pyramid is a square.

Surface area of a square pyramid = b2 + 2* b* s

This gives: Surface area of the square pyramid, SA= (3)2 + (2 * 3 * 5) = 9+ 30= 39m2

Therefore, the surface area of the given square pyramid is 39m2

Example 2: What is the surface area of a rectangular pyramid which has a base length of 6m, base width of 4m and a slant height of 8m?

Given: base length, l= 6m, base width, w = 4m

Slant height of the pyramid, s = 8m

Since it is a rectangular pyramid, the base of the 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= (6* 4) + (6* 8) + (4* 8) = 104m2

Therefore, the surface area of the given rectangular pyramid is 104m2