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.
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.
Fold R and S up to the centre line EO, so that they meet to form
a straight line and make a pentagon.
If you make 12 pentagons in this way and assemble them, using
your 'flaps' and 'pockets', you can make a dodecahedron.
If you use A4 paper for this
construction and try to make regular pentagons there is a small
error in the angle at E. Find this error and find the dimensions of
the paper which you would need to use to get an accurate regular
pentagon and hence an accurate regular dodecahedron.
1) You can construct other platonic solids
using paper and this
article explains how.
2) Have a look at the
October 2000 Article titled Classifying Solids using Angle
3) You can download a demo version
of Stella , a computer program which lets you create and view
polyhedra on the screen, then print out the nets required to build
your own models out of paper. Small Stella and Great Stella are
available from the Stella Website.
4) Alternatively, print out the models from
pdf available at the British
Crystallographic Association's Website