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At a Glance

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

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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.

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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: Challenge Level:1

okra
$ABCDE$ 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 $BE$.


The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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