Area - squares and rectangles

How many centimetres of rope will I need to make another mat just like the one I have here?

Cut off three right angled isosceles triangles to produce a pentagon. With two lines, cut the pentagon into three parts which can be rearranged into another square.

Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of the pictures.

Which has the greatest area, a circle or a square, inscribed in an isosceles right angle triangle?

Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.

If I use 12 green tiles to represent my lawn, how many different ways could I arrange them? How many border tiles would I need each time?

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.