### Areas and Ratios

What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.

### Six Discs

Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases?

Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the area enclosed by PQRS.

# Symmetric Angles

##### Stage: 4 Short Challenge Level:
See all short problems arranged by curriculum topic in the short problems collection

The diagram has rotational symmetry of order four about $D$.

If angle $ABC$ is $15^{\circ}$ and the area of $ABEF$ is $24$cm$^2$, what is the length of $CD$?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.