UK Secondary (7-11)
Border battles (Investigation)
Lesson

Straighten the Border

Suppose an island is divided as follows:

However, we want to straighten the border without changing the area of either territory.

Discussion Question

Is it possible to straighten the border without changing the area of either territory?

Activity
• Individually for five minutes, try to straighten the border without changing the area of either territory.
• In pairs or small groups, discuss and figure out a way to straighten the border without changing the area of either territory.
Question

Is there more than one way to straighten the border without changing the area of either territory? If so, find another way to draw the border.

We have already seen that the area of the triangle is calculated by the following formula:

$A=\frac{1}{2}bh$A=12bh

Knowing this, is there a way to change the shape of the triangle without changing the area of the triangle? Yes there is! The trick is to keep the base and height the same.