Area of Polygons (Using Decomposition)

Area is a measure of the space inside a 2D object.

I can measure the sides of the rectangle, and then find the area using the formula length times width.

I can break the shape into two rectangles. I can find the area of each rectangle and add the areas together to find the area of the bigger shape.

I can draw lines to break a rectangle into other rectangles, squares, triangles, and other polygons.

The total area of all of the shapes is equal to the area of the original rectangle.

The area of a right triangle is half the area of a rectangle with the same base and height.

I can break a parallelogram into two identical right triangles and a rectangle. When I combine the two triangles it forms a new rectangle. The area of this set of shapes is the same as the area of a rectangle with a length and width the same as the length and height of the parallelogram.

I can divide a polygon into rectangles and right triangles. Then I can find the area of each of the smaller shapes and add them together to find the total area.

First I plot each point. The coordinates tell me the position of the point on the x-axis and the y-axis. After I plot each point, I connect the points to make a polygon. I need to connect the points with straight lines and make a closed shape.

I can find the area in the same way, by dividing the shape into rectangles and triangles and finding the total area of those shapes.