How to Calculate the Square Foot of an Irregular Polygon

Find the Area of Irregular Polygons in Square Feet
••• Jupiterimages/ Images

Regular polygons are shapes made of straight lines with certain relationships among their lengths. For instance, a square has 4 sides, all the same length. A regular pentagon has 5 sides, all the same length. For these shapes, there are formulas for finding the area. But for irregular polygons, which are made of straight lines of any length, there are no formulas, and you need to be a little creative to find the area. Fortunately, any polygon may be divided into triangles, and there is a simple formula for the area of triangles.

    Label the vertices (points) of the polygon starting with 1 at an arbitrary vertex and continuing clockwise around the polygon. There should be as many vertices as there are sides. E.g. for a pentagon (five sides) there will be five vertices.

    Draw a line from vertex 1 to vertex 3. This will make one triangle, with vertices 1, 2, and 3. If there are only 4 sides, it will also make a triangle with vertices 1, 3 and 4.

    If the polygon has more than 4 sides, draw a line from vertex 3 to vertex 5. Continue in this way until you run out of vertices.

    Compute the area of each triangle. The formula for the area of a triangle is 1/2 * b * h, where b is the base and h is the height.

    Add up the areas, and this is the area of the polygon.

Related Articles

Montessori-Inspired Toys & Kits for Your Little Scientist
How to Find the Dimensions of a Square With the Area
How to Calculate the Apothem of a Polygon
How to Convert Square Dimensions to Round
How to Find Dimensions in Geometric Shapes
How to Calculate the Perimeter of a Diamond
How to Calculate Length of Sides in Regular Hexagons
How to Describe a Shape in Terms of Its Area and Perimeter
How To Calculate The Area of an Irregular Shape
Interesting Facts About Triangles in Math
How to Solve a Hexagon
How to Bisect a Triangle
How to Count Rectangles on a 5X5 Grid
How to Find the Perimeter of a Right Triangle
How to Calculate the Base of a Shape
Formula for the Volume of a Hexagon
How to Calculate the Surface Area of a Cylinder
How to Find the Area & Width of a Rectangle
Formula for the Volume of a Octagon
How to Measure the Length of the Diagonal Line of a...
How to Find the Lateral Area of a Square Pyramid