Upload
shze-hwa-lee
View
47
Download
0
Embed Size (px)
Citation preview
PYRAMID
- made up by connecting a base to an apex
apex
FORMULA
1/3 x BASE AREA x HEIGHT
Types of Pyramid
TriangularPyramid
Square Pyramid
Pentagonal Pyramid
½ x h x b
s x s
½ x a x pa= apothemp= perimeter
BASEPYRAMIDFORMULA OF BASE AREA
Example of Triangular Pyramid
Find the volume of the following triangular pyramid (correct to 1 decimal place):
Find the area of the base:
[continued]
• Sketch the base triangle and calculate its area solution:
[continued]
Sketch the side triangle and calculate pyramid height H
[continued]
Example of Square Pyramid
• Find the volume of a square pyramid with a height of 3 cm and a side length of 2 cm.
[continued]
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 cmb = 7 cmh = 11 cm
Volume of a pentagonal pyramid= 5/6 x abh
= 5/6 × 5 cm × 7 cm × 11 cm
= 320.833 cm3
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
Volume of a truncated
square pyramid
FormulaV = 1/3 (a2 + ab + b2 ) h
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: