# Perimeter and Area

### Blue and White

##### Stage: 3 Challenge Level:

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:

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:

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:

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:

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

### Fence It

##### Stage: 3 Challenge Level:

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

### Perimeter Challenge

##### Stage: 3 Challenge Level:

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

### Isosceles Triangles

##### Stage: 3 Challenge Level:

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:

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:

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:

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

### Warmsnug Double Glazing

##### Stage: 3 Challenge Level:

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.