Outside the Box Geometry
# Introduction

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**:

**True or False?**

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

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