# Problem of the Day: 2/8/13

In the figure below, the side length of the octagon is 4 cm. What is the length of the diagonal shown? Express your answer in simplest radical form.

Solution to yesterday’s problem:

We can imagine a diagonal going across the square which also serves as a diameter of the circle. The diagonal would split the square into two right triangles, and we could find the length of the diagonal using the Pythagorean Theorem.

$(6)^2+(6)^2=x^2$

$36+36=x^2$

$72=x^2$

$x=6\sqrt{2}$ (after simplification)

You may recognize this as a 45-45-90 triangle, in which case you didn’t have to do all that work. Anyway, if the diagonal/diameter is $6\sqrt{2}$ inches, then the radius will be half that, or $3\sqrt{2}$ inches.