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Outside the Box Geometry

Fun, challenging geometry that will shake up how you think and problem solve!

Strategic Geometry


You might not know the techniques needed to solve all of the puzzles in this challenging collection - but that’s why you’re here, right?

If you don’t know how to approach a given puzzle, 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!

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?

At first, you paint your \(1 \text{ in }\times 1\text{ in } \times 1\text{ in}\) cube blue on all sides. You then cut it into smaller cubes and paint all 8 completely pink.

What is the difference between the amount of blue paint you use and the amount of pink paint, in square inches?

What is the length of the red perimeter of this figure?

Two overlapping circles, with centers \(A\) and \(B,\) form the figure above. Line segment \(\overline{AB}\) is a radius of both circles.


1) The circumference of a circle of radius \(1\) is \(2\pi.\)

2) Slice it up like two overlapping pizzas!

This twelve pointed star is made by extending the sides of a regular 12-sided polygon (a dodecagon). What is the measure of the pink angle?

True or False?

Connecting the midpoints of the four sides of any simple quadrilateral makes a parallelogram.


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