Earlier today I set you five puzzles from More Geometry Snacks. Here are the questions each followed by two methods of solution. Sometimes the simple action of drawing in a few extra lines reveals the solution clearly.
1. A point inside a square is connected to its four vertices. What fraction of the square is shaded?
2. A shaded region is constructed within an equilateral triangle using the midpoint A of a side, and the midpoint between AB. What fraction is shaded?
3. In this regular hexagon, three diagonals have been drawn to form this parallelogram. What fraction of the hexagon is shaded?
4. A square is shown with its inscribed and circumscribed circle. What fraction of the larger circle is shaded?
r2 = R2/2
5. This last puzzle is about angles. Four identically-sized squares are arranged in an L. What’s the angle marked in blue?
Solution: 45 degrees
I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
Thanks to Ed Southall and Vincent Pantaloni for today’s puzzles.