Triangular pyramid is a three-dimensional figure with four triangular bases.

The volume of a pyramid in cubic units. The length of the triangular base is 'a' and 'H' is the height, distance from the base to the apex and 'h' be the slant height.

The volume of a triangular pyramid is:

V =

$\frac{1}{3}$ A H

A = Area of the triangular base.

H = D

istance from the base to the apex.(Height).Here

Area of the triangular base (A) =

$\frac{1}{2}$ah

=> Volume of Pyramid =

$\frac{1}{3}$ * (

$\frac{1}{2}$ah) * H

=

$\frac{1}{6}$ahH.

**Formula:**

V = $\frac{1}{6}$ahH

Where,

V = Volume of the triangular pyramid.

a = Side of the triangular base.

h = Slant height or Apothem length.

H = Height of the pyramid, distance from the base to the apex.

Example:Find the volume of the triangular pyramid with the side 12 cm, slant height 10 cm and height of the pyramid is 17 cm.

Solution:

**Step 1:**Side of the triangular base = 12 cm

Slant height of the triangular pyramid = 10 cm

Height of the pyramid (H) = 17 cm

Step 2: Area of the triangular base =

$\frac{1}{2}$base * height

=> A =

$\frac{1}{2}$ * 12 * 10

= 60

=> A = 60 cm

^{2}

Step 3:Volume of the triangular pyramid (V) = $\frac{1}{3}$AH=> V =

$\frac{1}{3}$ * 30 * 17

= 170 cm

^{3} .

Hence the volume of the triangular pyramid is 170 cm

^{3} .answer