# Three Squares in a Square +-- {.image} [[ThreeSquaresinaSquare.png:pic]] > Three equal squares are packed into this bigger square. What's the shaded area? =-- ## Solution by [[Similar Triangles]] +-- {.image} [[ThreeSquaresinaSquareLabelled.png:pic]] =-- With the points labelled as above, let $a$ be the length of a side of a smaller square and let $b$ be the distance between the squares. These are then two of the sides of triangle $E D C$. Triangle $C B A$ then has shorter sides of lengths $a$ and $a + b$. Since these two triangles are [[similar]], the ratios $a : b$ and $a + b : a$ are equal, meaning that $a b + b^2 = a^2 = 5$. The shaded region can be viewed as the square $H F B A$ without the two triangles $H G A$ and $C B A$. The combined area of these triangles is $a (a + b)$ meaning that the shaded region has area $b(a + b) = 5$.