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Surface Area of a Pyramid Formula

A pyramid is a polyhedron with a polygonal base and triangular faces equal to the number of sides in the base. All the triangular faces meet at a single point called the apex. The faces of the pyramid connect the bases with the apex. If the pyramid is oblique leaning to one side or the base is irregular, there is no straightforward way to find the surface area. Each triangular face will be a different shape and size, so you would have to find the area of each using whatever measurements you are given.

Types of Pyramids

There are many types of Pyramids, and they are named after the shape of their base. Surface Area of a Pyramid is the sum of the area of the polygonal base and the area of the triangular faces.


Types of Pyramid



The Surface Area of a Pyramid Formula is given as,
    Surface Area of a Square Pyramid Formula
Surface Area of a Triangular Pyramid Formula
Surface Area of a Pentagonal Pyramid Formula
Surface Area of a Hexagonal Pyramid Formula

Where,
a - apothem length of the pyramid.
b - base length of the pyramid.
s - slant height of the pyramid. 

Related Calculators
Surface Area of a Pyramid Calculator Surface Area of a Square Pyramid
Calculate Surface Area Calculate Surface Area of a Circle
 

Surface Area of a Pyramid Problems

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Some solved problems on the surface area of a pyramid are given below :

Solved Examples

Question 1: Find the surface area of a hexagonal pyramid of apothem length 3 cm, base length 5 cm, and slant height 10 cm ?
Solution:
 
Given,
a = 3 cm
b = 5 cm
s = 10 cm

Surface area of a hexagonal pyramid
3ab + 3bs
= (3 $\times$ 3 cm $\times$ 5 cm) + (3 $\times$ 5 cm $\times$ 10 cm)
= 45 cm2 + 150 cm2
= 195 cm2

 

Question 2: Find the surface area of a pentagonal pyramid of apothem length 9 cm, base length 12 cm, and slant height 21 cm ?
Solution:
 
Given,
a = 9 cm
b = 12 cm
s = 21 cm

Surface area of a pentagonal pyramid
$\frac{5}{2}$ab + $\frac{5}{2}$bs

= $\frac{5}{2}$(9 cm $\times$ 12 cm) + $\frac{5}{2}$(12 cm $\times$ 21 cm)

= 270 cm2 + 630 cm2
= 900 cm2
 

More topics in Surface Area of a Pyramid Formula
Surface Area of a Square Pyramid Formula
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