Geometry I

Which purple polygon does not have the same area as the others?

If you don’t know how to approach a puzzle in this set, spend a minute using your intuition to make an informed guess. Then be sure to check out the solution to learn a technique that can be used to solve it precisely!

Strategic Geometry


The two squares are identical in size, the four small circles are identical in size, and every circle touches either other circles or squares in all places they appear to be touching.

Which area is larger, that of the yellow region on the left or the purple region on the right?

Strategic Geometry


A five-pointed star is made by extending the sides of a regular pentagon. What fraction of the star on the right is shaded yellow?

Strategic Geometry


A square has line segments connecting corners to midpoints, as shown. What fraction of the larger square is colored green?

Strategic Geometry


In the diagram, the smaller circles are identical and are both centered on the larger circle's diameter.

Which has a larger area, the top blue region or the yellow circle?

Strategic Geometry


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