Perimeter and Area

Curvy Areas

Stage: 4 Challenge Level: Challenge Level:1

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

Triangles and Petals

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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: Challenge Level:1

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

Salinon

Stage: 4 Challenge Level: Challenge Level:1

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

Arclets

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".