Pick A Shape

Some shapes are so awkward, that the only way to find their area seems to be to break the shape down into lots of smaller triangles and rectangles and work all these out separately. Until 1899, and a Mr Pick spotted an alternative approach…

The Problem: 

Find the areas of the shapes below.

In the first group of shapes, they all contain a single ‘interior’ dot.

What’s the connection between the area and the number of dots on the perimeter?

 

 What difference does the addition of one extra interior dot make to your formula?

 

 How about a formula for 5 interior dots?

(Hint: 4 more than the very first examples you did) 

The Big One:

 Use your formula to calculate the area of this, extremely awkward, shape: 

 

Open the File as a Word Document

 

Send site mail to admin@1000problems.org  or personal comments direct to sdakeyne@psc.ac.uk with questions or comments about this web site.
Last modified: June 18, 2007