Area - squares and rectangles

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
Four or five

Age

11 to 14

Challenge level

The diagram shows a large rectangle composed of 9 smaller rectangles. If each of these rectangles has integer sides, what could the area of the large rectangle be?
problem
Televisual technology

Age

14 to 16

Challenge level

If a new and an old television have screens of the same area, what is the ratio of their widths?
problem
Flower show

Age

14 to 16

Challenge level

How long will it take six gardeners to dig six circular flower beds?
problem
Eyelids

Age

14 to 16

Challenge level

Can you work out the shaded area surrounded by these arcs?
problem
Proof of Pick's theorem

Age

16 to 18

Challenge level

Follow the hints and prove Pick's Theorem.
problem
Griddy region

Age

14 to 16

Challenge level

Weekly Problem 34 - 2008
What is the area of the region common to this triangle and square?
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?
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
Sizing them up

Age

5 to 7

Challenge level

Can you put these shapes in order of size? Start with the smallest.