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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.

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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.

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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.

At a Glance

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Is it?