Similar Shade Sails

Difficulty:
intermediate

Rating:
4-stars

GCSE Marks:
3-marks

GCSE Text:
Two triangular sun shades are mathematically similar and have the following dimensions:
similar triangles.png

a)  What is the length of side DE on the larger shade?

The area of triangle ABC is 3m².

b)  What is the area of triangle DEF?

Suggestions:
This is a simple problem involving similar shapes. Students will need to read the questions carefully and calculate the side scale factor. Question b) often raises healthy discussion as to the approach, as some students tend to find the perpendicular height of the smaller triangle, whilst others remember the ‘area’ and ‘volume’ rules of similar shapes. It normally takes only 2-3 minutes for the class to solve.

Extension Ideas:
Teachers could extend the learning by considering:

  • An ‘Extra Large’ shade (draw as JKL) is advertised as having an area of 12m².  What are the dimensions of the base and sides on the extra large shade?

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