# Four Regular Polygons +-- {.image} [[FourRegularPolygons.png:pic]] > The area of two of these regular polygons has been given. Can you find the area of the red triangle? =-- ## Solution by [[Congruent Triangles]] +-- {.image} [[FourRegularPolygonsLabelled.png:pic]] =-- In the diagram above, the lengths of $A B$ and $A D$ are the same, as are the lengths of $A C$ and $A E$. Angles $B \hat{A} D$ and $C \hat{A} E$ are equal, so the angles $B \hat{A} C$ and $D hat{A} E$ are equal. This means that triangles $B A C$ and $D A E$ are [[congruent]], and so $C B$ and $E D$ have the same length. Since the triangles are [[equilateral]], they are therefore congruent and so the area of the red triangle is also $3$. ## Solution by [[Transformation]] The rotation that is centred on $A$ that takes $B$ to $D$ also takes $C$ to $E$, and so triangles $A C B$ and $A E D$ are [[congruent]].