*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* .

Does this work for any whole number side lengths?

If not, under what circumstances does it work?

What if the lengths of the sides of the triangles had been *a* and *b* instead of 3 and 4?

Can you construct an equilateral triangle whose area is the sum of the areas of *ABC* and *DEF*? What is the new area?

Mathematical reasoning & proof. Circle properties and circle theorems. Creating and manipulating expressions and formulae. Sine rule & cosine rule. Pythagoras' theorem. Making and proving conjectures. Regular polygons and circles. Sine, cosine, tangent. Generalising. Area - triangles, quadrilaterals, compound shapes.