Dimension and Area I

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This is a unit square. It is the foundation of all linear and area measurement concepts in plane Geometry. The basic unit (u) could be 1 centimeter, 1 inch, 1 cubit, 1 hand-span, 1 chain, etc…

The square unit (u²) would then be square centimeters, square inches, square cubits, square hand-spans, square chains, etc…

Take a look at the following rectangle. Each small square in the diagram is a unit square.

The dimensions in base five notation are 23_fiveu x 12_fiveu. The area can be determined by imagining base five area pieces filling up the rectangle...

The area needs to be regrouped...

The area of the rectangle in base five notation would be 331_five u², because that's the number of area units regrouped in base five. So, we have a 23_fiveu x 12_fiveu rectangle with an area of 331_fiveu².

You can think of the area in other bases, too. How about trying it in base three? Or base seven?

Here are a couple of more problems to try out. Have fun with dimension and area!

Try to sketch the rectangles the following clues describe, and determine the missing information:

• A rectangle whose area is 242_five. What are its dimensions?
• A rectangle with area of 134_five and one dimension of 4_five. What is the other dimension?
• A rectangle with area of 222_five, and one dimension of 20_five. What is the other dimension?

We'll use these concepts of area and dimension to explore the basic operations with base five models in the next several lessons. See you there!