# Subdivided Triangle +-- {.image} [[SubdividedTriangle.png:pic]] > Red segments have length $5$, and yellow segments have length $3$. What's the shaded area? =-- ## Solution by [[Pythagoras' Theorem]] and [[Crossed Trapezium]] +-- {.image} [[SubdividedTriangleLabelled.png:pic]] =-- Since the yellow segments have length $3$ and the red have length $5$, the side lengths of the triangle are $6$, $8$, and $10$. These satisfy $10^2 = 6^2 + 8^2$ which means that triangle $A D C$ is [[right-angled triangle|right-angled]] by the converse to [[Pythagoras' Theorem]]. As $E$ is the [[midpoint]] of $A D$ and $B$ of $A C$, $E B$ is [[parallel]] to $D C$ and so $E B C D$ is a [[trapezium]]. With the diagonals, this makes a [[crossed trapezium]]. The scale factor from $E B$ to $D C$ is $2$, so the area of the trapezium is $(1 + 2)^2 = 9$ times the area of triangle $E G B$. Since $E B$ has length $4$, $D C$ length $8$, and $E D$ has length $3$ the area of the trapezium is $18$ so triangle $E G B$ has area $2$. Then triangle $E G D$ has area $4$.