Areas 1 Regular Figures Mathematical Formulae Method of

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