At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

Pent

The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.

Dodecawhat

Follow instructions to fold sheets of A4 paper into pentagons and assemble them to form a dodecahedron. Calculate the error in the angle of the not perfectly regular pentagons you make.

Pentakite

Stage: 4 and 5 Challenge Level:

 $ABCDE$ is a regular pentagon of side length one unit. $BC$ produced meets $ED$ produced at $F$. Show that triangle $CDF$ is congruent to triangle $EDB$. Find the length of $BE$.