![Kissing Triangles](/sites/default/files/styles/medium/public/thumbnails/content-97-12-six3-icon.jpg?itok=a-3qrMB6)
Area - triangles, quadrilaterals, compound shapes
![Kissing Triangles](/sites/default/files/styles/medium/public/thumbnails/content-97-12-six3-icon.jpg?itok=a-3qrMB6)
![Dividing the Field](/sites/default/files/styles/medium/public/thumbnails/content-97-04-six1-icon.jpg?itok=oDb73xEB)
problem
Dividing the Field
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?
![Doesn't add up](/sites/default/files/styles/medium/public/thumbnails/content-97-03-six3-icon.jpg?itok=nUZvwIt5)
problem
Doesn't add up
In this problem we are faced with an apparently easy area problem,
but it has gone horribly wrong! What happened?
![Equilateral Areas](/sites/default/files/styles/medium/public/thumbnails/content-97-02-six5-icon.jpg?itok=rybnQ981)
problem
Equilateral Areas
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.
![Diagonals for Area](/sites/default/files/styles/medium/public/thumbnails/content-02-10-15plus2-icon.gif?itok=MhQRr2w0)
problem
Diagonals for Area
Can you prove this formula for finding the area of a quadrilateral from its diagonals?
![Golden Triangle](/sites/default/files/styles/medium/public/thumbnails/content-01-09-15plus3-icon.gif?itok=hzFeJC6p)
problem
Golden Triangle
Three triangles ABC, CBD and ABD (where D is a point on AC) are all isosceles. Find all the angles. Prove that the ratio of AB to BC is equal to the golden ratio.
![Six Discs](/sites/default/files/styles/medium/public/thumbnails/content-01-02-15plus4-icon.gif?itok=9h5ZOL0B)
problem
Six Discs
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?
![So Big](/sites/default/files/styles/medium/public/thumbnails/content-00-07-15plus2-icon.jpg?itok=f06Dwphz)
problem
So Big
One side of a triangle is divided into segments of length a and b
by the inscribed circle, with radius r. Prove that the area is:
abr(a+b)/ab-r^2
![Biggest Bendy](/sites/default/files/styles/medium/public/thumbnails/content-00-06-15plus2-icon.jpg?itok=LV-urVag)
problem
Biggest Bendy
Four rods are hinged at their ends to form a quadrilateral. How can you maximise its area?
![Areas and Ratios](/sites/default/files/styles/medium/public/thumbnails/content-00-04-15plus2-icon.png?itok=KCcw922_)
problem
Areas and Ratios
Do you have enough information to work out the area of the shaded quadrilateral?