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Outside the Box Geometry

# 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?

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!

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? (The line segment $$\overline{AB}$$ is the radius of both circles, and the circumference of a circle is $$2\pi r ).$$

Hint:

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

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