Investigation 1: Sum of Areas
The first step of the sequence above is formed by \(4\) congruent equilateral triangles. If the area of the big equilateral triangle is \(1\) unit\(^2\), then the area of the blue triangle is \(\large\frac{1}{4}\) unit\(^2\).
a) What is the area of the new blue triangle in step \(2\)?
b) What is the sum of the areas of the blue triangles in step \(3\)?
c) Imagine what the figure would look like in step infinity. If you added up all of the areas of the blue triangles in step
infinity, what would be a sum that is too high? What would be a sum that is too low?
d) Challenge: What is the sum of the areas of the blue triangles in step infinity?
Investigation 2: Game Set Flat
Click the image below and enter class code 6VWWK or the class code from your teacher.
a) What is the area of the new blue triangle in step \(2\)?
b) What is the sum of the areas of the blue triangles in step \(3\)?
c) Imagine what the figure would look like in step infinity. If you added up all of the areas of the blue triangles in step
infinity, what would be a sum that is too high? What would be a sum that is too low?
d) Challenge: What is the sum of the areas of the blue triangles in step infinity?
Investigation 2: Game Set Flat
Click the image below and enter class code 6VWWK or the class code from your teacher.