It’s the second Thursday in December, and so time for the second Chalkdust Christmas competition. Throughout this month, we are running a series of competitions, with a fantastic prize up for grabs in each one. This week’s prizes are copies of *More geometry snacks* by Ed Southall and Vincent Pantaloni.

*More geometry snacks* is a book stuffed full of really good geometry puzzles, and would make an excellent Christmas present for your maths-loving friends and family. If you’re not lucky enough to win a copy, you can order them here.

But before we get on to how to win this week’s prize, it’s time to announce last week’s winners. The prizes on offer last week were three *Festival of the spoken nerd* box sets and the winners were:

Name |
Favourite equation containing $\pi$ |

Mike Fuller | $\displaystyle\pi=\frac\tau2$ |

David Kendel | $\displaystyle\frac\pi4 = 1 – \frac13 + \frac15 – \frac17 + \frac19 – … $ |

Alex Bolton | $\displaystyle\int_{-\infty}^{\infty} \mathrm{e}^{-\frac{x^2}2} dx = \sqrt{\pi}$ |

The prizes will be on their way shortly!

Right, on to this week’s competition. To win a copy of *More geometry snacks*, solve the following puzzle and enter your answer in the form below.

The picture below shows a Christmas tree that we have constructed. We started by drawing a circle inside a square, then drew three triangles and one rectangle: the three triangles are contained entirely within the circle, and the rectangle goes a tiny bit outside the circle. The three triangles and the rectangle all have the same height.

The lines marked with single and double arrows are pairs of parallel lines.

The tree is made up of three green triangles (branches) and a brown rectangle (the trunk). The area of the circle is $16\pi$. What is the area of the tree?

*To enter this competition, enter your name, email address and answer in the form below before 23:59 on Wednesday 19 December. The winners will then be randomly chosen from the correct answers and announced alongside next week’s puzzle.*