The document discusses different types of pyramids and formulas for calculating their volumes. It covers triangular, square, pentagonal, right, oblique, and truncated square pyramids. Formulas are provided for calculating the volume of each type of pyramid based on attributes of the base like its area or perimeter and the height. Examples are also given of applying the formulas to find the volume of different pyramids given their dimensions.

1. PYRAMID
- made up by connecting a
base to an apex
apex
FORMULA
1/3 x BASE AREA x HEIGHT

2. Types of Pyramid
Triangular
Pyramid
Square
Pyramid
Pentagonal
Pyramid
½ x h x b
s x s
½ x a x p
a= apothem
p= perimeter
BASEPYRAMID
FORMULA OF
BASE AREA

3. Example of Triangular
Pyramid
Find the volume of the following triangular
pyramid (correct to 1 decimal place):
Find the area of the base:

4. [continued]
• Sketch the base triangle and calculate its area
solution:

5. [continued]
Sketch the side triangle and calculate pyramid height H

6. [continued]

7. Example of Square
Pyramid
• Find the volume of a square pyramid with a height of 3
cm and a side length of 2 cm.

8. [continued]

9. Example of Pentagonal
Pyramid
• Find the volume of a pentagonal pyramid of apothem length
5 cm, base length 7 cm and height 11 cm ?
• Solution:
Given,
a = 5 cm
b = 7 cm
h = 11 cm
Volume of a pentagonal pyramid
= 5/6 x abh
= 5/6 × 5 cm × 7 cm × 11 cm
= 320.833 cm3

10. RIGHT vs. OBLIQUE Pyramid
- tell us where the top (apex) of the pyramid is
- when the apex is directly above the center of
the base it is a Right Pyramid, otherwise it is an
Oblique Pyramid.
Right Pyramid Oblique Pyramid

11. Volume of a truncated square
pyramid
Formula
V = 1/3 (a2 + ab + b2 ) h

12. Example of Truncated
square pyramid
Calculate the lateral area, surface area and volume of the
truncated square pyramid whose larger base edge is 24 cm,
smaller base edge is 14 cm and whose lateral edge is 13 cm.
Solution: