Area - squares and rectangles

problem
Numerically equal

Age

7 to 11

Challenge level

Can you draw a square in which the perimeter is numerically equal to the area?
problem
Rope mat

Age

7 to 11

Challenge level

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

Age

14 to 16

Challenge level

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.
problem
Framed

Age

11 to 14

Challenge level

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.
problem
Compare areas

Age

14 to 16

Challenge level

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

Age

7 to 11

Challenge level

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

Age

5 to 11

Challenge level

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?
problem
Making boxes

Age

7 to 11

Challenge level

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

Age

7 to 11

Challenge level

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?
problem
Great squares

Age

7 to 11

Challenge level

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