Being resourceful - geometry

A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

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

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

How many winning lines can you make in a three-dimensional version of noughts and crosses?

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

How many different symmetrical shapes can you make by shading triangles or squares?

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?