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Home » Math » Area of Polygons on a Geoboard

Area of Polygons on a Geoboard

What is the area of this concave polygon?

Maye there is a formula out there to figure it out, but we are going to use our brains instead.  It’s going to be hard, but it’s going to be fun!

First let’s make a rectangle around the whole polygon.  This tells us that the polygon is going to be less than 12 square inches.

Now let’s splice and dice.

The blue triangle in that yellow rectangle is 1.5 square inches.

The blue triangle in this yellow square equals 2 square inches. (Click here for how we figure out areas of triangles.)

The area of this blue triangle is 2 square inches.  Plus I need to add the 1 square inch from that square in the upper right corner.

Now I have 1.5 + 2 + 2 + 1 = 6.5 square inches.

Hard, but fun, right?


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