Area of shade sails (intermediate)

Difficulty:
intermediate

Rating:
4-stars

GCSE Marks:
4-marks

GCSE Text:
Two triangular shade sails are suspended above a patio to provide shade from the sun.  The total area of shade that they provide is 13.75m².  The dimensions of these sails are shown here:
shade-sails-2

What is the perpendicular height of the smaller triangular shade?

Suggestions:
A reverse area question which will test the students’ ability to work an area back to find one of the dimensions. Students often needs encouraging not to give up on this, so it’s a good one to test resilience.  Some exam boards will also award marks for correct units on a question like this, so it is a good idea to stress correct units in the final answer.

Extension Ideas:
Teachers could extend the learning by considering:

  • On the hottest of days, the shade sails stretch a little, so each dimension is increased by 10%. Calculate the total area again, and explain why it has not increased by 10%.

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