Question 54

Challenge question #54 (03/07/2017)

Junior Question

Maths Image A calisson is a French sweet that looks like two equilateral triangles glued together.
Maths Image Calissons are packed into regular hexagonal boxes, arranged in a way such that there are no gaps between them like in the diagram alongside.
So, there are $3$ distinct orientations for the calissons in a box: Maths Image

For any arrangement of the calissons of side length $1$, find the proportion of each orientation of calisson in a box with side length $6$.

Answer

Senior Question

Maths Image A circle with radius $x$ cm is inscribed within a square as shown. A line [MN] is drawn where M is the midpoint of [AD] and N is the point on [BC] such that BN $= \tfrac{1}{3}$ NC.

Find the shaded area in terms of $x$.

Answer