section_path: Area formulas/Polygon formulas/Dissection, parallelograms, and triangles
section_name: Dissection, parallelograms, and triangles
paragraph_text: Dissection, parallelograms, and triangles
  
  Most other simple formulas for area follow from the method of dissection.This involves cutting a shape into pieces, whose areas must sum to the area of the original shape.For an example, any parallelogram can be subdivided into a trapezoid and a right triangle, as shown in figure to the left. If the triangle is moved to the other side of the trapezoid, then the resulting figure is a rectangle. It follows that the area of the parallelogram is the same as the area of the rectangle:
  
  However, the same parallelogram can also be cut along a diagonal into two congruent triangles, as shown in the figure to the right. It follows that the area of each triangle is half the area of the parallelogram:
  
  Similar arguments can be used to find area formulas for the trapezoid as well as more complicated polygons.