Perimeter and Area

Blue and White

Stage: 3 Challenge Level: Challenge Level:1

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

Can They Be Equal?

Stage: 3 Challenge Level: Challenge Level:1

Sometimes area and perimeter of rectangles are taught separately, and are often confused. In this problem students consider the relationship between them.

Changing Areas, Changing Perimeters

Stage: 3 Challenge Level: Challenge Level:1

Working on this problem will give students a deeper understanding of area and perimeter, and how they change as a shape is altered.

Perimeter Possibilities

Stage: 3 Challenge Level: Challenge Level:1

This problem combines both area and perimeter by inviting students to consider the different possibilities for the perimeter when the area of a rectangle is fixed.

Triangles in a Square

Stage: 3 Challenge Level: Challenge Level:1

What are the possible areas of triangles drawn in a square?

Fence It

Stage: 3 Challenge Level: Challenge Level:1

This problem challenges students to work systematically while applying their knowledge of areas of rectangles.

Perimeter Challenge

Stage: 3 Challenge Level: Challenge Level:1

Can you deduce the perimeters of the shapes from the information given?

Isosceles Triangles

Stage: 3 Challenge Level: Challenge Level:1

This problem encourages students to use coordinates, area and isosceles triangles to solve a non-standard problem. To find all possible solutions they will need to work systematically.

Pick's Theorem

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

This problem allows students to consolidate their understanding of how to calculate the area of irregular shapes, while offering an opportunity to explore and discover an interesting result.

An Unusual Shape

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

On the Edge

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

If you move the tiles around, can you make squares with different coloured edges?

Warmsnug Double Glazing

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This problem offers students a chance to develop strategies for organising and understanding mixed up information within the context of calculating areas and perimeters of rectangles.