Area - squares and rectangles

M is the midpoint of the side of the rectangle. What is the area (in square units) of the triangle PMR?

How many ways can you find of tiling the square patio, using square tiles of different sizes?

I cut this square into two different shapes. What can you say about the relationship between them?

This quadrilateral has an unusual shape. Are you able to find its area?

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

This diagram has symmetry of order four. Can you use different geometric properties to find a particular length?

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

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

Weekly Problem 33 - 2006
A square is inscribed in an isoscles right angled triangle of area $x$. What is the area of the square?

Weekly Problem 44 - 2009
A garden has the shape of a right-angled triangle. A fence goes from the corner with the right-angle to a point on the opposite side. How long is the fence?