Frustum of a Regular Pyramid Formula
When we chop off the top of a regular pyramid what we get is known as the frustum of a regular pyramid. This is why it is also called a truncated pyramid. Distance between top and bottom is the height of the pyramid and is denoted by “h”. “L” is the slant height of the pyramid. There are two bases ( top and bottom), whose area is denoted by A_{1} and A_{2}. We use the frustum of a regular pyramid formula for finding the total surface area for the frustum of a regular pyramid, the lateral surface area for the frustum of a regular pyramid and, the volume for the frustum of a regular pyramid. Let us learn more about the frustum of a regular pyramid formula along with solved examples.
What is Frustum of a Regular Pyramid Formula?
There are three general formulas for the frustum of a regular pyramid, as given below.
 Formulas for total surface area for frustum of a regular pyramid
Total surface area = \(\dfrac{1}{2}(P_1+ P_2)\times L + A_1+ A_2\)
 Formulas for lateral surface area for frustum of a regular pyramid
Lateral surface area = \(\dfrac{1}{2}(P_1+ P_2)\times L\)
 Formulas for volume for frustum of a regular pyramid
Volume = \(\dfrac{1}{3}h ( A_1+ A_2+ \sqrt{A_1A_2})\)
Here,
P_{1} and P_{2} = Perimeter of bases
h = height
A_{1} and A_{2} area of bases
L= slant height
Solved Examples Using Frustum of a Regular Pyramid Formula

Example 1:
Find the volume of the frustum of a regular pyramid whose area of bases are 10 square units^{ }and 12 square units respectively and height is 11 units.
Solution:
To find: The volume of a frustum of a regular pyramid.
Given,
A_{1} = 10 square units
A_{2} = 12 square units
h = 11 unitsUsing Volume formula for Frustum of a Regular Pyramid,
\(\text{Volume}= \dfrac{1}{3}h ( A_1+ A_2+ \sqrt{A_1A_2})\)
\(\text{Volume}= \dfrac{1}{3}\times11\times ( 10+ 12+ \sqrt{10\times 12})\)
\(\text{Volume}= \dfrac{362.49}{3}\)
V = 120.83 cubic units
Answer: The volume of a frustum of a regular pyramid is 120.83 cubic units.

Example 2:
A frustum of a regular pyramid has perimeters of the top and bottom surfaces as 20 cm and 30 cm, respectively. The slant height of the pyramid is 24 cm. Calculate lateral surface area.
Solution:
To find: Lateral surface area of a frustum of a regular pyramid.
Answer: The lateral surface area of the frustum of a regular pyramid is 600 cm^{2}.
Given,
P_{1} = 20 cm
P_{2} = 30 cm
L = 24 cm
Using formula of lateral surface area of frustum of a regular pyramid,
\(\text{Lateral surface area} = \dfrac{1}{2}(P_1+ P_2)\times L\)
\(\text{Lateral surface area} = \dfrac{1}{2}(20+ 30)\times 24\)
Lateral surface area = 600 cm^{2}