Area - triangles, quadrilaterals, compound shapes

problem
Quadrilaterals in a square

Age

11 to 14

Challenge level

What's special about the area of quadrilaterals drawn in a square?
problem
The farmers' field boundary

Age

11 to 14

Challenge level

The farmers want to redraw their field boundary but keep the area the same. Can you advise them?
problem
Triangle in a trapezium

Age

11 to 16

Challenge level

Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?
problem
Equilateral areas

Age

14 to 16

Challenge level

ABC and DEF are equilateral triangles of side 3 and 4 respectively. Construct an equilateral triangle whose area is the sum of the area of ABC and DEF.
problem
Doesn't add up

Age

14 to 16

Challenge level

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?
problem
Arrowhead

Age

14 to 16

Challenge level

The points P, Q, R and S are the midpoints of the edges of a non-convex quadrilateral.What do you notice about the quadrilateral PQRS and its area?
problem
Of all the areas

Age

14 to 16

Challenge level

Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?
problem
Rhombus in rectangle

Age

14 to 16

Challenge level

Take any rectangle ABCD such that AB > BC. The point P is on AB and Q is on CD. Show that there is exactly one position of P and Q such that APCQ is a rhombus.
problem
Overlap

Age

14 to 16

Challenge level

A red square and a blue square overlap. Is the area of the overlap always the same?
problem
Pick's theorem

Age

14 to 16

Challenge level

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.