top of page


Learning Intention:


To understand how sails work. To be able to calculate the area and perimeter of a triangle.

How do sails work? Thanks to Design Squad for the video



Have you seen a sail before?  What do they do and why are they needed? What shape are sails?  Why are they that shape?


Early sails were square, but the problem with that is that was that the direction the boats could sail was limited. They needed to use oars and paddles to go against the wind - upwind.


As technology improved, sails began to be cut differently, into the more familiar triangular shape we see today.


How do sails work?


When a boat is sailing downwind, that is, with the wind behind it, the sail catches the wind and the boat is blown forward.  When the wind is coming from the side, the sail operates like an airplane wing, with the wind blowing across it. This creates a force called lift.  The sails are curved, just like an airplane wing and this creates a pressure difference between the windward side (the side that catches the wind) and the leeward side (the opposite side).  This pressure difference is what drives the boat forward.


The curve is built into the sail by the sailmaker, through accurate cutting and sewing of the narrow panels that make up the sail.

Activity:  Measuring surface area of sails.



  • Paper

  • Rulers


We are going to calculate the area and perimeter of a sail. This is one way we can use math in other parts of our life.


What are some of the reasons sailors may want to calculate the area of sails? What would be some benefits of increasing or reducing the sail area?



  1. Draw a diagram on the board of a triangular sail and label the parts.  Foot, head, luff, leech, tack and clew.

  2. How do we measure the perimeter of a sail?  Measure the luff, leech and foot and add them together.

  3. How do we measure the area of a sail?  Put the formula on the board. ½  Base (Foot) x Height (Luff)  Show them a rectangle is made up of 2 triangles.

  4. Give the students a piece of paper for them to draw their sail.

  5. Label the parts and measure the perimeter and areas of their sail.

  6. Compare their sail measurements with others.  How will the different size sails affect the boat’s speed?  What could you do to depower the sail?


Use their sail as an art project and decorate or make it look authentic, adding a number, insignia, eyelets, woolies etc.  Cut it out and use it for the ‘Sail Away’ activity.


Take another piece of paper and make a sail with some curve in it.  Cut out panels like a sailmaker would and tape them together to create a curved sail.  Use this sail in the ‘Sail Away’ activity.




Sail, hēra.


Buoyancy, puhautanga - The ability of something to float in a liquid.


Displacement - The moving of something from its place.


Life jacket, kahu kautere.


Upwind - Sailing in the opposite direction in which the wind is blowing.

Downwind - Sailing in the direction in which the wind is blowing.


Force - A push or pull on an object.

Windward - The side of a boat that is facing the wind.


Leeward - The side of the boat that is sheltered from the wind.


Luff - The front or the leading edge of a sail.


Leech - The back edge of a sail.

Foot (of a sail) - The bottom edge of the sail.


Woolies - Or tell-tales are the strips of ribbon or wool on the side of a sail.


Waka - A traditional Māori canoe.

Kevlar - A very strong synthetic fibre used to make sails and bullet proof vests.


Carbon fibre - A very strong lightweight synthetic fibre used for high performance products like sails, boats and aeroplanes.

bottom of page