Cutting Corners

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

Four Triangles Puzzle

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

Transformations on a Pegboard

How would you move the bands on the pegboard to alter these shapes?

Uncanny Triangles

Stage: 2 Challenge Level:

Why do this problem?

This problem needs a systematic approach. It is useful when learners are studying the area of right-angled triangles. It is important to remember that it is only the two shorter sides of the triangles that are being considered in the problem, not all three sides.

Most learners will need to draw some right-angled triangles on squared paper to get a feel for the problem.

Key questions

Where is a good place to start?

Have you looked at some of the examples given in the problem?

Do you need to draw all possible triangles to see if any meet the requirements?

If you double the length of the sides how does the area change?

Possible extension

Learners could consider fractional measures or look for triangles where the sum of the three sides is numerically equal to the area.

Possible support

Suggest drawing some right-angled triangles on squared paper and counting the squares to find the area.

Visualising. Area. Combinations. Right angled triangles. Working systematically. Interactivities. Multiplication & division. Addition & subtraction. Factors and multiples. Investigations.

You may also like