# Pyramid Formula

A polyhedron that has a polygonal base and triangles for sides, is a pyramid. The three main parts of any pyramid’s: apex, face and base. The base of a pyramid may be of any shape. Faces usually takes the shape of an isosceles triangle. All the triangle meet at a point on the top of the pyramid that is called “Apex”.

The formula for finding the volume and surface area of the pyramid is given as,

$\large Surface\;Area\;of\;a\;Pyramid=Base\;Area+\frac{1}{2}\left(Number\;of\;Base\;Sides \times Slant\;Height \times Base \;Length \right)$

$\large Volume\;of\;a\;Pyramid=\frac{1}{2} \times Base\;Area \times Height$

### Square Pyramid

A Pyramid with a square base, 4 triangular faces and an apex is a square pyramid.

The Square Pyramid formulas are,

$\large Base\;Area\;of\;a\;Square\;Pyramid=b^{2}$

$\large Surface\;Area\;of\;a\;Square\;Pyramid=2bs+b^{2}$

$\large Volume\;of\;a\;Square\;Pyramid=\frac{1}{3}b^{2}h$

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

### Triangular Pyramid

Triangular pyramid is said to the pyramid where it has triangular faces, triangular.

The Triangular Pyramid formulas are,

$\large Base\;Area\;of\;a\;Triangular\;Pyramid=\frac{1}{2}\:ab$

$\large Surface\;Area\;of\;a\;Triangular\;Pyramid=\frac{1}{2}\:ab+\frac{3}{2}\:bs$

$\large Volume\;of\;a\;Triangular\;Pyramid=\frac{1}{6}\:abh$

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

This pyramid has pentagonal base, with 5 sides , triangular faces and an apex.

The Pentagonal Pyramid Formulas are,

$\large Base\;Area\;of\;a\;Pentagonal\;Pyramid=\frac{5}{2}\:ab$

$\large Surface\;Area\;of\;a\;Pentagonal\;Pyramid=\frac{5}{2}\:ab+\frac{5}{2}\:bs$

$\large Volume\;of\;a\;Pentagonal\;Pyramid=\frac{5}{6}\:abh$

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

This pyramid has a hexagonal base with six sides, six triangular faces and an apex.

The Hexagonal Pyramid Formulas are,

$\large Base\;Area\;of\;a\;Hexagonal\;Pyramid=3ab$

$\large Surface\;Area\;of\;a\;Hexagonal\;Pyramid=3ab+3bs$

$\large Volume\;of\;a\;Hexagonal\;Pyramid=abh$

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.

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