Area - squares and rectangles

problem
Growing rectangles

Age

11 to 14

Challenge level

What happens to the area and volume of 2D and 3D shapes when you enlarge them?
problem
Expanding pattern

Age

11 to 14

Challenge level

How many squares are needed to continue this pattern?
problem
Crazy shading

Age

14 to 16

Challenge level

Can you work out the fraction of the larger square that is covered by the shaded area?
problem
Garden fence

Age

14 to 16

Challenge level

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?
problem
Symmetric angles

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

This quadrilateral has an unusual shape. Are you able to find its area?
problem
Cutting it out

Age

5 to 11

Challenge level

I cut this square into two different shapes. What can you say about the relationship between them?
problem
Mid-point area

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

Weekly Problem 29 - 2008
The seven pieces in this 12 cm by 12 cm square make a Tangram set. What is the area of the shaded parallelogram?
problem
Triangle in a hexagon

Age

11 to 14

Challenge level

Weekly Problem 3 - 2009
What fraction of the area of this regular hexagon is the shaded triangle?