# Four Squares in a Big Square +-- {.image} [[FourSquaresinaBigSquare.png:pic]] > Squares of the same colour are the same size. What's the total shaded area? =-- ## Solution by [[Properties of Squares]] +-- {.image} [[FourSquaresinaBigSquareLabelled.png:pic]] =-- The diagonal of the blue squares is half the side length of the outer square, which is $3$. Using the [[properties of a square]], the area of a blue square is therefore $4.5$. The sides of the blue square are at $45^\circ$ so form the diagonals of a square in the middle whose sides are the green lines and the sides of the red squares. This square is the same size as a red square, so the red squares have side length $2$ and area $4$. The total shaded area is therefore $17$.