Area - triangles, quadrilaterals, compound shapes

problem

Triangle Island

Age

7 to 11

Challenge level

You have pitched your tent (the red triangle) on an island. Can you move it to the position shown by the purple triangle making sure you obey the rules?
problem

Uncanny Triangles

Age

7 to 11

Challenge level

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
problem

Triangle Transformation

Age

7 to 14

Challenge level

Start with a triangle. Can you cut it up to make a rectangle?
problem

Dividing the Field

Age

14 to 16

Challenge level

A farmer has a field which is the shape of a trapezium as illustrated below. To increase his profits he wishes to grow two different crops. To do this he would like to divide the field into two trapeziums each of equal area. How could he do this?
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

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

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

Towering Trapeziums

Age

14 to 16

Challenge level

Can you find the areas of the trapezia in this sequence?
problem

Six Discs

Age

14 to 16

Challenge level

Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases?