Here are three different ways that you can find the area of an irregular polygon using a grid or coordinate plane:
1. (Top Left) You can break the polygon into right triangles and rectangles. Then, using the coordinates of each point, you can find the length of the base and height of each triangle and rectangle. Next, you can use the formulas for the area of a triangle and the area of a rectangle to find each area. Last, add up all of the areas to get the total area of the polygon.
2. (Top Right) You can beak the polygon into triangles only. Then use the distance formula to find the lengths of the bases of each triangle. Next, use the grid to determine the height of each triangle. Use the lengths of the bases and the heights of each triangle to find the area of each triangle using the formula for the area of a triangle. Add up the areas of the triangles to find the total area of the figure.
3. (Bottom Center) You can draw a rectangle around the polygon. Find the area of the rectangle. Then find the areas of the right triangles formed by the rectangle and the polygon. Next, sum up the areas of the triangles. Last, subtract the sum of the areas of the triangles from the area of the rectangle to find the total area of the polygon.