Similarity and congruence

What is the total area of the triangles remaining in the nth stage of constructing a Sierpinski Triangle? Work out the dimension of this fractal.

Try out this geometry problem involving trigonometry and number theory

A finite area inside and infinite skin! You can paint the interior of this fractal with a small tin of paint but you could never get enough paint to paint the edge.

Can you spot a cunning way to work out the missing length?

Equal touching circles have centres on a line. From a point of this line on a circle, a tangent is drawn to the farthest circle. Find the lengths of chords where the line cuts the other circles.

Make a poster using equilateral triangles with sides 27, 9, 3 and 1 units assembled as stage 3 of the Von Koch fractal. Investigate areas & lengths when you repeat a process infinitely often.

Given a regular pentagon, can you find the distance between two non-adjacent vertices?

Find the area of the shaded region created by the two overlapping triangles in terms of a and b?

Move the point P to see how P' moves. Then use your insights to calculate a missing length.