![Overlap](/sites/default/files/styles/medium/public/thumbnails/content-03-01-six4-icon.jpg?itok=L0JAB9ec)
Area - triangles, quadrilaterals, compound shapes
![Overlap](/sites/default/files/styles/medium/public/thumbnails/content-03-01-six4-icon.jpg?itok=L0JAB9ec)
![Square pizza](/sites/default/files/styles/medium/public/thumbnails/content-03-01-six2-icon.gif?itok=BpcQnLma)
problem
Square pizza
Can you show that you can share a square pizza equally between two
people by cutting it four times using vertical, horizontal and
diagonal cuts through any point inside the square?
![Rhombus in Rectangle](/sites/default/files/styles/medium/public/thumbnails/content-01-03-six5-icon.png?itok=nloeBwzi)
problem
Rhombus in Rectangle
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.
![Of all the areas](/sites/default/files/styles/medium/public/thumbnails/content-00-02-six4-icon.png?itok=x3m44zQ0)
problem
Of all the areas
Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?
![Linkage](/sites/default/files/styles/medium/public/thumbnails/content-99-02-six2-icon.png?itok=DNuAF4tt)
problem
Linkage
Four rods, two of length a and two of length b, are linked to form
a kite. The linkage is moveable so that the angles change. What is
the maximum area of the kite?
![Isosceles](/sites/default/files/styles/medium/public/thumbnails/content-98-12-six6-icon.jpg?itok=vVW7mRS_)
problem
Isosceles
Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas.
![Same Height](/sites/default/files/styles/medium/public/thumbnails/content-98-08-six5-icon.jpg?itok=MqNp9esL)
problem
Same Height
A trapezium is divided into four triangles by its diagonals. Can you work out the area of the trapezium?
![Arrowhead](/sites/default/files/styles/medium/public/thumbnails/content-98-07-six6-icon.jpg?itok=ff5ztzMJ)
problem
Arrowhead
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?
![Quad in Quad](/sites/default/files/styles/medium/public/thumbnails/content-98-06-six6-icon.jpg?itok=YI8HYOzo)
problem
Quad in Quad
Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?
![From all corners](/sites/default/files/styles/medium/public/thumbnails/content-98-03-six4-icon.jpg?itok=7uySrNCg)
problem
From all corners
Straight lines are drawn from each corner of a square to the mid
points of the opposite sides. Express the area of the octagon that
is formed at the centre as a fraction of the area of the square.