Triangle Island
3 out of 3
You have pitched your tent (the red triangle) on an island. Can you move it to the position shown by the purple triangle making sure you obey the rules?
Problem
You have pitched your tent (the red triangle) on an island. Can you move it to the position shown by the purple triangle? You must obey the following rules:
You can only move one peg (corner) at a time.
Pegs (corners) must stay on the island.
The area of your tent (the triangle) must always stay the same but the sides may stretch.
Getting Started
What is the area of the tent?
What will you have to make sure stays the same in order to keep the area of the tent the same?
Experiment by moving different pegs (corners) at a time.
You could print off a copy of the island to try out your ideas.
Student Solutions
Hugo sent us pictures of his solution. Well done, Hugo!
I know that the area of a triangle is given by the forumula \[ \frac{1}{2} \times base \times height.\] The original triangle has base $1$ and height $1$, so as long as each triangle on the way also has base $1$ and height $1$ the area will stay the same".
Teachers' Resources
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
Why do this problem?
Key questions
Possible extension
Some children might like to draw their own island on squared paper and 'pitch' their own tents.