maths pyramid

12
PYRAMID - made up by connecting a base to an apex apex FORMULA 1/3 x BASE AREA x HEIGHT

Upload: xennechau

Post on 06-Aug-2015

131 views

Category:

Education


0 download

TRANSCRIPT

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: