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How to find the area of rectilinear figures (Polygons)

Updated: Jul 12, 2021

Have you wondered how to find area of rectilinear figures? Or how do we actually find the area of complex figures such as quadrilaterals, pentagon, hexagon? The list goes on... Are there any formulas for them?

Today, Math Lobby is going to help you understand how to get the area of rectilinear figures using the shoelace method. Have fun!

In case you missed out on our previous article on how to find area of triangles without having base and perpendicular height, do visit our link How To Find Area Of Triangles Without Perpendicular Base Or Height to learn more.

How to find area of rectilinear figures (polygons)

The formula for finding the area of a triangle using the coordinates of the vertices can be modified and applied to a quadrilateral figure:

Therefore, the general formula can be given as such:

where the vertices (x1, y1), (x2, y2), (x3, y3), … (xn, yn) are in an anticlockwise direction.

Let’s take a look at the application of this formula in the example question shown below:

Question: Find the area of the quadrilateral with vertices at P (-2, 2), Q (0, 5), R (3, 5) and S (1, 0).


Area of PQRS = ½ {[(0) (2) + (-2) (0) + (1) (5) + (3) (5)] – [(5) (-2) + (2) (1) + (0) (3) + (5) (0)]}

= ½ [(0 + 0 + 5 + 15) – (-10 + 2 + 0 + 0)]

= ½ [(20) – (-8)]

= 14 units^2

And that’s all for today, students! Math Lobby hopes that after this article, you have a clear understanding on the application of the formula to find the area of rectilinear figures involving triangles and polygons, and is able to solve relevant questions!

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