Summation of Accumulative Physical Quantity

Areas of plane shapes can be determined by integration when the area of a plane shape is expressed as an infinitesimal area element that can be summed by the application of integration. 

Areas of plane shapes 

1. Area of Rectangle

   

   Area by integration.

   

2. Area of Square

   Area of square is a special case of rectangle. The area of square can be obtained by letting b=a

   

3. Area of Parallelogram

   

   Area of parallelogram by horizontal summation approach

   

   Area of parallelogram by vertical summation approach

   

4. Area of Triangle

   For right angle triangle

   

   Area of right angle triangle by horizontal summation approach

   

   For oblique triangle

   

   Area of oblique triangle by area between curves

   

5. Area of Rhombus

   

   Area of rhombus by area between curves

   

6. Area of Trapezoid

   

   Area of trapezoid by area between curves