Area - squares and rectangles

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

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

Proof of Pick's Theorem

Age

16 to 18

Challenge level

Follow the hints and prove Pick's Theorem.
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.
article
From One Shape to Another

Read about David Hilbert who proved that any polygon could be cut up into a certain number of pieces that could be put back together to form any other polygon of equal area.