Four diagonals of a regular octagon with side length 2 intersect as shown. Find the area of the shaded region.

michaelcai
Aug 25, 2017

#1**+2 **

The triangle just to the left of the blue area is a 45-45-90 triangle....and the side opposite the 90° angle has a length of 2√2 units = √8 units

And the blue area is a parallelogram with equal sides of this length

And the acute angle in the parallelogram = 45°

So....its area =

2 * (1/2) (√8)^2 sin (45°) =

8 / √2 units^2 = 8 √2 / 2 units^2 = 4 √2 units^2

CPhill
Aug 25, 2017