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”.

Pyramid

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.

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.

Pentagonal PyramidThe 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.

Hexagonal Pyramid

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.


Practise This Question

Which of the following is an example of perpendicular lines?

1. Corners of your circular room floor

2. One of the angles in both your set squares

3. Angle included between the hour hand and minute hand when it is 12:15 in your wall clock