Calculation of Pyramid Surface Area
Table of Contents
Surface Area of a Pyramid
A pyramid is a 3D structure with a flat base connected at the top, which is called the apex. There are different types of pyramids such as triangular, square, pentagonal, which refers to the shape of the base.
The surface area of a pyramid is the sum of the base and sides (number of sides depends on the shape of the base).
This article will go over an example calculation for the surface area of a square pyramid.
A square shaped pyramid has a square base and triangular faces on each side.
The area of the base will be a x a = a2 (area of square)
The surface area is the sum of the areas of the base and all sides.
The surface area of the pyramid sides is the determined through the slant (s) height and base length (a). (area of a triangle is 1/2 x base x height, as there are 4 sides, the total area of the sides are 2*a*s) .
Total surface area = a2 + 2*a*s
If we have the vertical height of the pyramid, this can be \(a^2 + 2a \sqrt {(a/2)^2 + h^2}\)
Formula for Surface area of a Pyramid = a2 + 2*a*s or \(a^2 + 2a \sqrt {(a/2)^2 + h^2}\)
Surface Area of a Square Pyramid Example 1
A square pyramid has base length of 22 cm at the base and a slant height of 15 cm. What is the surface area of the pyramid?
Solution:
The surface area of a pyramid formula is a2 + 2*a*s
Surface area = (222) + (2*22*15) = 1144 cm2
This can also be written as 0.1144 m2 (1144 multiplied by 10-4 to convert from cm2 to m2).
Note – remember to check units when calculating the surface area.
Surface Area of a Pyramid Example 2
A pyramid has base length of 150 mm at the base and a vertical height of 225 mm. What is the surface area of the cone?
Solution:
The surface area of a pyramid equation is \(a^2 + 2a \sqrt {(a/2)^2 + h^2}\)
Surface area = \(150^2 + 2*150 \sqrt {(150/2)^2 + 225^2}\) = 93,651 mm2
This can also be written as 0.093651 m2 (93,651 multiplied by 10-6 to convert from mm2 to m2).
Note – remember to check units when calculating the surface area.