Compute correct to two decimal places.

The picture shows the vertices of a regular hexagon connected by lines.

i) Prove that the inner red hexagon is also regular.

ii) How much of a side of the large hexagon is a side of the small hexagon?

iii) How much of the area of the large hexagon is the area of the small hexagon?

Prove that Use this to compute correct to two decimal places.

Prove that Can you find other numbers like this?

The picture shows a tan gram of 7 pieces made by cutting a square of side 4 centimetres. Calculate the length of the sides of each piece.