Math 9 Honors Shoe Lace method:

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

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:

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

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

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

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

Ratios of a Trapezoid