# Perimeter and Area

### Curvy Areas

##### Stage: 4 Challenge Level:

This problem offers students the opportunity to calculate areas of parts of circles and use $\pi$ in calculations.

### An Unusual Shape

##### Stage: 3 Challenge Level:

This problem offers the opportunity to practise calculating areas of circles and fractions of a circle in the context of an optimisation task.

### Triangles and Petals

##### Stage: 4 Challenge Level:

This problem offers the opportunity to practise calculating arc lengths, working in terms of $\pi$, and calculating interior angles of regular polygons

### Track Design

##### Stage: 4 Challenge Level:

This problem offers an authentic context within which to calculate arc lengths and requires students to present their findings in a convincing manner.

### Blue and White

##### Stage: 3 Challenge Level:

In the four examples below identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?