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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.

The Pyramid Formula in general is given as,

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

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

The Square Pyramid formulas are,

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

## Triangular Pyramid

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

The Triangular Pyramid formulas are,

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

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

The Pentagonal Pyramid Formulas are,

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

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

The Hexagonal Pyramid Formulas are,

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

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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