Area of-parallelogram

1.           What is the area of this parallelogram?

2.                       Start by adding some construction lines

3.                       The area of the parallelogram is that of the large rectangles less the areas of four triangles and two rectangles

4. Now let’s separate out the pieces and focus on the four triangles and two rectangles

5.                 And let’s bring the two congruent triangles together

6.             The total area of these four shapes is  

7. The area of the parallelogram is that of the large rectangles less the areas of four rectangles:  

8.           So the area of this parallelogram is    

9. 2 dimensional vector product We define the vector product between two vectors in two dimensions by where is the angle from to . This is equal to the area of the parallelogram formed from the two vectors.      

10. Area of a parallelogram Start with a triangle Now put two copies together and you can see that the area of the parallelogram is         The height of the triangle is So the area of the triangle is