In a right angled triangular field, three animals are tethered to posts at the midpoint of each side. Each rope is just long enough to allow the animal to reach two adjacent vertices. Only one animal. . . .

If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

A tennis ball is served from directly above the baseline (assume the ball travels in a straight line). What is the minimum height that the ball can be hit at to ensure it lands in the service area?

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Follow the instructions and you can take a rectangle, cut it into 4 pieces, discard two small triangles, put together the remaining two pieces and end up with a rectangle the same size. Try it!

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

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?

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

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