Students will learn how to find the diagonal length of a rectangle, given the length of each side. They must already know the Pythagorean theorem. Here's a video demonstration of this lesson. Give your students problems involving both squares and rectangles. Students should notice the diagonal length is irrational, except when the side and diagonal lengths form a Pythagorean triple. Next, give your students this challenge:

Two 4x4 squares intersect at right angles, bisecting their intersecting sides, as shown. The circle's diameter is the segment between the two points of intersection. What is the area of the shaded region?

Here's the solution.Conclude by giving your students this challenge:

Find the side length of the square:

Here's the solution.

Next, give your students these challenges:

- Shaping It by NRICH
- Double Your Popcorn, Double Your Pleasure by NRICH

Conclude by leading this investigation:

Daedalus and Icarus try to Escape

by MathPickle