1. Math 9 Honors Shoe Lace method:

2. What is the Shoe Lace Method?
The shoe lace method is a process for finding the area of any polygon when you have the coordinates of the vertices
Place the coordinates in a column, starting in a CW direction
Make sure you repeat the first coordinate that was used
Multiply diagonally for each column
Add each column:
Subtract the columns and divide by 2 to get the area

3. Practice: Find the area of the following shape:
Place the coordinates in a column, starting in a CW direction
Subtract the columns and divide by 2 to get the area
Make sure you repeat the first coordinate that was used
Multiply diagonally for each column
Add each column:

4. Why the Shoe Lace Method Works? (Part 1)
The first part of understanding why the Shoe Lace Method works is knowing what a “Determinant” is:
When given two coordinates (a,b) and (c,d), the determinant is: A1

5. Determinant: ½(bc-ad)
Half the determinant of (a,b) and (c,d) will give the area of the triangle created by these two points and the origin
If the coordinates are switched, the area becomes negative
Just take the absolute value to get the area

6. How the Shoe Lace Method Works (Part 2)
When we use the shoe lace method, we are taking the determinant multiple times

7. Practice: Find the area of the shaded regions:
Find the point of intersection first
Diagonal #1:
Diagonal #2:
Solve for Intersection point

8. Ratios of a Trapezoid