Triangular Pyramid Geometry

In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex forms a triangle. It is a conic solid with polygonal base. A pyramid with an n-sided base will have n + 1 vertices, n + 1 faces, and 2n edge.
Source from wikipedia)

geometry triangular pyramid:

A triangular pyramid is a pyramid having a triangular base.Here we are going to study about triangular pyramid in geometry and example problems.

Formulas:

Surface area of triangular pyramid = A + `(3/2)` s*l
Here A = area of base = `1/2` * a*s
volume of triangular pyramid = `(1/6)` a*b*h

Here,

a represent the apothem

s,b is the sides of the pyramid

l is the slant height

h is the height of the pyramid.

Triangular pyramid geometry - example problems.

Example: 1

Find the surface area of the triangular pyramid with side 7 meter ,slant height is 9 meter and apothem length is 8 meter.

Solution:

We know the formula for surface area of the triangular pyramid = A + `(3/2)` sl

First we have to find the area of base A = `1/2` * a*s

Here a = 8 meter, s = 7 meter substitute the above formula we get

A = `1/2 ` * 8 * 7

A = `1/2` *56

A = 28 meter square

Now we find the surface area of the triangular pyramid

S.A = 28 + `(3/2)` * 7 * 9

= 28 + `(3/2)` *63

Simplify the above we get

= 28 + `189/2`

= 28 + 94.5

= 122.5 meter square

Therefore the surface area of the triangular pyramid = 122.5 meter square


Triangular pyramid geometry - example: 2

Find the volume of the triangular pyramid with height is 11 meter ,base is 9 meter and apothem length is 12 meter .

Solution:

We know the formula for volume = `(1/6)` abh

Here h = 11 meter, b = 9 meter, a = 12 meter substitute this value into the formula we get

Volume =  ` (1/6)` 12 * 9 * 11

Volume = `(1/6) ` 1188

Simplify the above we get

Volume = 198 meter3

Therefore the volume of the triangular pyramid is 198 meter3