Areas 1 Regular Figures Mathematical Formulae Method of
- Slides: 32
Areas 1. Regular Figures • Mathematical Formulae • Method of Coordinates 2. Irregular Figures • Graphical Method • Give and Take Method • Trapezoidal Rule • Simpson’s One-Third Rule
Area is divided into triangles, rectangles, squares or trapeziums Area of the one figure (e. g. triangles, rectangles, squares or trapeziums) is calculated and multiplied by total number of figures
Mathematical Formulae
Mathematical Formulae
Areas by Method of Coordinates
Areas by Method of Coordinates
Areas by Method of Coordinates
Areas by Method of Coordinates
Areas by Method of Coordinates Area = 0. 5(| 136840. 01 – (-84890. 94) |) = 110865. 48 ft 2
Areas Irregular Figures • Give and Take Method • Graphical Method • Trapezoidal Rule • Simpson’s One-Third Rule
Give and take Method In this method, the irregular figure is replaced by a regular one of approximately equal area that can be calculated by one of the methods explained earlier.
Graphical Method Area=( number of compelet squer* area of each squer)+ (area of the uncompelet sqer
Graphical Method =1 cm 2
Trapezoidal Rule
Trapezoidal Rule
Trapezoidal Rule
Example
Example
Offset Simpson’s One-Third Rule Intercept ONLY used with Odd number of offsets (i. e. Even number of Intercepts)
Simspon’s One-Third Rule
Example
Areas with mechanical Tools
Planimeters Digital Planimeter Optical Polar Planimeter
Planimeters
From internet : Measure areas using Google Maps http: //www. acme. com/planimeter/
Calculate area with computer
Scanner the map then calculate the area by specialized program
By Auto cad
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