### Areas and Ratios

What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.

### 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?

Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the area enclosed by PQRS.

# Trapezium Four

##### Stage: 4 Challenge Level:
You may wish to use GeoGebra to explore this problem.

What makes a shape a trapezium ?

The diagonals of a trapezium divide it into four parts.

• Can you create a trapezium where two of those parts are equal in area?

• Can you create a trapezium where three of those parts are equal in area?

• Can you create a trapezium where all four parts are equal in area?

In each case can you explain how much freedom you have?

Or, if any of those challenges are impossible say why you think that.