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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 take the shape of an isosceles triangle. All the triangles 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,

\[\large Surface\;Area\;of\;a\;Pyramid=Base\;Area+\frac{1}{2}\left(Number\;of\;Base\;Sides \times Slant\;Height \times Base \;Length \right)\]
\[\large Volume\;of\;a\;Pyramid=\frac{1}{3} \times Base\;Area \times Height\]

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

A triangular pyramid is a type of pyramid with triangular faces and a triangular base.

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

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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  1.  Asis Kumar De
    December 30, 2019 at 12:51 pm

    If we cut the at certain height from the apex point, then what will be the height of the balance cut pyramid. Bottom section is 2070 x 2070, top section is 250 x 250 and volume is 800000000 cubic mm

    Reply