Area - squares and rectangles

article
Exploration versus calculation

This article, written for teachers, discusses the merits of different kinds of resources: those which involve exploration and those which centre on calculation.
article
Approaches to area

This article for teachers gives some food for thought when teaching ideas about area.
problem
Trig rules OK

Age

16 to 18

Challenge level

Change the squares in this diagram and spot the property that stays the same for the triangles. Explain...
problem
Semicircle stack

Age

14 to 16

Challenge level

What is the total area enclosed by the three semicicles?
problem
3x3 areas

Age

11 to 14

Challenge level

Which of the following shaded regions has an area different from the other shaded regions?
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
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
Expanding pattern

Age

11 to 14

Challenge level

How many squares are needed to continue this pattern?
problem
Arc area

Age

14 to 16

Challenge level

What is the area of the shape enclosed by the line and arcs?
problem
Geoboards

Age

7 to 11

Challenge level

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.