### 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.

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.

### Get Cross

A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?

# Six Discs

##### Stage: 4 Challenge Level:

Six circular discs, all of radius 1 unit, are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box.

• Without using any calculations, compare the areas of the bases of boxes A and B and say which is the larger.
• Use estimation to list the packings in order of increasing base area. Which are the hardest to put in order?
• Now calculate the area of the base of each box and compare the correct order with your estimate.