The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?
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.
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.
This problem is taken from the UKMT Mathematical Challenges.