Conclude by giving your students these challenges:
- Ben's Game by NRICH
- 2019 Math Kangaroo Levels 11-12 Problem #30 by STEM4all
- In the Bag by NRICH
- 2015 AMC 8, Problem 25
Find the area of the green region:
Here's the solution: First, notice the center of the circle and the bottom right of the quadrant, are opposite corners of a square. Next, notice the quadrant is comprised of the square, plus 3/4 of the circle, plus twice the green region. The area of the square is \(2,\) the area of \(3/4\) of the circle is \((3/2)\pi,\) and the area of the quadrant is \(\pi(3/2 + \sqrt{2}).\) Removing the area of the \(3/4\) circle and the area of the square from the quadrant, we're left with twice the green area. Dividing this by \(2\) gives us the area of the green region, which is \((\pi\sqrt{2})/2 - 1.\)