Area of boat sails (Pythag)

Difficulty:
intermediate

Rating:
4-stars

GCSE Marks:
4-marks

GCSE Text:
When comparing sailing boats, the larger the sails, the more wind is caught so the faster the boat generally travels. Here are the designs for 3 sail boats.

sail-design-higher

Which boat has the largest overall sail area, and is therefore likely to travel the fastest?

Suggestions:
This has proven to be a popular video for students of a wide range of ages and abilities. Discussions are often healthy around which dimensions/measurements they should use to find the area of a triangle, and what the formula is.  Boat C has a hidden problem of a missing sail height, so students should be encouraged to spot the pattern of triangle side/hypotenuse, or use Pythagoras. It normally takes 5-8 minutes to solve, and of course in a GCSE question of this type, method marks would be awarded even the final answer isn’t correct due to an arithmetic error.

Extension Ideas:
Teachers could extend the learning by considering:

  • Boat C has a ‘jib sail’ which can be deployed in addition to the main sails. This extra sail adds 20% to the sail area. Would that make a difference to which boat is likely to travel the fastest?
  • Boat D has a single sail with an area of 33m². It has a mast which allows the vertical measurement of the sail to be 12m in height. What is the horizontal dimension of that sail?

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