# maths pyramid

Post on 06-Aug-2015

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1. 1. PYRAMID - made up by connecting a base to an apex apex FORMULA 1/3 x BASE AREA x HEIGHT
2. 2. Types of Pyramid Triangular Pyramid Square Pyramid Pentagonal Pyramid x h x b s x s x a x p a= apothem p= perimeter BASEPYRAMID FORMULA OF BASE AREA
3. 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. 4. [continued] Sketch the base triangle and calculate its area solution:
5. 5. [continued] Sketch the side triangle and calculate pyramid height H
6. 6. [continued]
7. 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. 8. [continued]
9. 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. 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. 11. Volume of a truncated square pyramid Formula V = 1/3 (a2 + ab + b2 ) h
12. 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: