What fraction of this regular decagon is shaded? Give this problem a try before jumping in for the solution! Solution: Brute Force The first solution is done with trigonometric functions. We first let each side length of the decagon equal 1. We then add two straight lines as shown below. The size of the angles can…

I was walking by the cathedral in town today and found out it was Ash Wednesday today thanks to the congregation of people sat at the front of the church, waiting for the liturgy to commence. So out of curiosity, I took a seat and had my first ever Ash Wednesday liturgy. When the priest…

So we have a star, a mountain and another shape today. Our job is to carefully count all the triangles in each of them. I encourage you to give this problem a try, and when you are ready, keep reading for the solution. Solution Of course there are 5 triangles. But there’s more! This is…

Honestly please share your approach to this one in the comments below because there are at least 7 different ways you can get to the correct answer. It’s also a good exercise in reviewing your trigonometry fundamentals. So dig in, my friend! And when you are done trying, keep reading for the solution. Solution Because…

You are making clown hats from a circular piece of cardboard. The circumference of the base of each hat equals its slant height,which in turn is equal to the radius of the piece of cardboard. What is the maximum number of hats that you can make fromthe piece of cardboard? As usual, I encourage to…

The shaded figure is formed by eight circular arcs of equal radius. Four arcs are centered at the vertices of a square, and the other four at the midpoints of its sides. The diagonals of the square have length 1. Find the total length of the boundary of the shaded figure. As usual, I encourage…