Problem of the Week

Problem 28

Let A be the length between a regular polygon’s centre to one of it’s vertices. An example of A is shown above for a regular hexagon.

a) Show that the area of a regular hexagon can be represented by $\frac{3\sqrt3}{2}A^2$ .

b) Similarly, show that the area of a regular dodecagon (12-sided polygon) can be represented by $3A^2$ .

c) Can an expression of the area be derived for a regular n-sided polygon, in terms of $n$ and $A^2$ ?

d) $\frac{3\sqrt3}{2}$ $\approx$ 2.598. As the number of sides in a regular polygon increases, the coefficient of $A^2$ increases. State what the coefficient of $A^2$ approaches as the number of sides in a regular polygon increases more and more.

Submit a solution!

Name

School / Institution

Details

Upload solution (*.jpg, *.pdf, *.docx, *.png accepted, max 2mb)

Publish consent

You can display my name on the CMS website if I successfully solve the problem.

Data Protection

I consent to providing this information to Cambridge Maths School. It will be processed in accordance with the Trust Privacy Policy.

Problem of the Week

Problem 28

Submit a solution!

Site Search