Challenge Level

Shape C is a parallelogram with a base of 2 and a height of 3.

Can you use the two pictures below to work out the area of the parallelogram?

Here are two more parallelograms made by *shearing *a rectangle with a base of 2 and a height of 3.

Can you draw similar diagrams to work out their areas?

Use the GeoGebra applet below to explore other parallelograms with a base of 2 and a height of 3.

What do you notice? Can you explain it?

Explore other families of parallelograms with a particular base and height, by moving the red and green dots.

**Can you come up with a general rule for working out the area of a parallelogram if you know its base and height? Can you explain why your rule works?**

I wonder what happens when we shear triangles...

Here is a family of four sheared triangles with a base of 1 and a height of 2.

**Can you work out the area of the triangles?**

You might like to use the GeoGebra applet below to help.

Explore other families of triangles with a particular base and height.

**Can you come up with a general rule for working out the area of a triangle if you know its base and height?**

**Can you explain why your rule works?**