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Pyramid Formula

Pyramid is a polyhedron with a polygonal base and triangles for sides. There are three important parts in any pyramid namely: base, face and apex. The base of the pyramid may be of any shape. The faces of the pyramid are mostly isosceles triangle. All the triangular faces meet at a single point called the apex.


Pyramid


The Pyramid Formula in general is given as,
Surface Area of A Pyramid Formula
Volume of A Pyramid Formula

Pyramids are of different types. They are named based on the the base shape of pyramid. The types of pyramid are: square pyramid, triangular pyramid, pentagonal pyramid and hexagonal pyramid.

Related Calculators
Pyramid Calculator Area of a Pyramid Calculator
Pyramid Volume Calculator Square Pyramid Volume Calculator
 

Square Pyramid

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A Square Pyramid has a square base, 4 triangular faces and an apex :


Square Pyramid


The Square Pyramid formulas are,
Base Area of a Square Pyramid Formula
Surface Area of a Square Pyramid Formula
Volume of a Square Pyramid Formula

Where,
b - base length of the square pyramid.
s - slant height of the square pyramid.
h - height of the square pyramid.

Triangular Pyramid

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A Triangular Pyramid has a triangular base, 3 triangular faces and an apex




The Triangular Pyramid formulas are,
Base Area of a Triangular Pyramid Formula
Surface Area of a Triangular Pyramid Formula
Volume of a Triangular Pyramid Formula

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

Pentagonal Pyramid

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A Pentagonal Pyramid has a pentagonal base, 5 triangular faces and an apex


Pentagonal Pyramid


The Pentagonal Pyramid Formulas are,
Base Area of a Pentagonal Pyramid Formula
Surface Area of a Pentagonal Pyramid Formula
Volume of a Pentagonal Pyramid Formula

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

Hexagonal Pyramid

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A Hexagonal Pyramid has a hexagonal base, 6 triangular faces and an apex :


Hexagonal Pyramid


The Hexagonal Pyramid Formulas are,
Base Area of a Hexagonal Pyramid Formula
Surface Area of a Hexagonal Pyramid Formula
Volume of a Hexagonal Pyramid Formula

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

Pyramid Problems

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Some solved problems on pyramid are given below :

Solved Examples

Question 1: Find the base area, surface area and volume of a triangular pyramid of apothem length 3 cm, base length 6 cm, height 10 cm and slant height 12 cm ?
Solution:
 
Given,
a = 3 cm
b = 6 cm
h = 10 cm
s = 12 cm

Base area of a triangular pyramid
= $\frac{1}{2}$ab

= $\frac{1}{2}$ $\times$ 3 cm $\times$ 6 cm

= 9 cm2

Surface area of a triangular pyramid
= $\frac{1}{2}$ab + $\frac{3}{2}$bs

= $\frac{1}{2}$ $\times$ (3 cm) $\times$ (6 cm) + $\frac{3}{2}$ $\times$ (6 cm) $\times$ (12 cm)

= 9 cm2 + 108 cm2
= 117 cm2

Volume of a triangular pyramid
= $\frac{1}{6}$abh

= $\frac{1}{6}$ $\times$ 3 cm $\times$ 6 cm $\times$ 10 cm

= 30 cm3

 

Question 2: Find the base area, surface area and volume of a hexagonal pyramid of apothem length 5 cm, base length 8 cm, height 12 cm and slant height 15 cm ?
Solution:
 
Given,
a = 5 cm
b = 8 cm
h = 12 cm
s = 15 cm

Base area of a hexagonal pyramid
3ab
= 3 $\times$ 5 cm $\times$ 8 cm
= 120 cm2

Surface area of a hexagonal pyramid
3ab + 3bs
= (3 $\times$ 5 cm $\times$ 8 cm) + (3 $\times$ 8 cm $\times$ 15 cm)
= 120 cm2 + 360 cm2
= 480 cm2

Volume of a hexagonal pyramid
abh
= 5 cm $\times$ 8 cm $\times$ 12 cm
= 480 cm3
 

More topics in Pyramid Formula
Volume of a Pyramid Formula Surface Area of a Pyramid Formula
Triangular Pyramid Formula Regular Square Pyramid Formula
Hexagonal Pyramid Formula Frustum of a Regular Pyramid Formula
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