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.
- If you can do it one way, try to do it another way too.

- In pairs or small groups, discuss and figure out a way to straighten the border without changing the area of either territory.

#### Follow-up Questions

- 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.
- Use the applet below to show your new straight border. Slide the blue dots to make a new border and see how the areas change. Reveal the straight line to see if your points are indeed all on a straight line.

- Compare your new border with one of your peers.
- We have already seen that the area of the triangle is calculated by the following formula:

$A=\frac{1}{2}bh$`A`=12`b``h`

Knowing this, is there a way to change the shape of the triangle without changing the area of the triangle?