A pre-school tot or elementary school student can easily calculate the area of plane geometric structures imposed on a background subdivided into equal squares -- such as a pegboard or tiles on floor or wall. The trick involves COUNTING SQUARE-CORNERS ON THE BOUNDARY OF THE STRUCTURE (BOUNDARY POINTS) AND THOSE INTERIOR TO THE STRUCTURE (INTERIOR POINTS).

Let i = number of boundary points; let b = mumber of interior points; let A = structure's area in square units. Then we have the FORMULA:

		A = i + b/2 - 1

I'll use astericks for the corners of the squares in the structure I draw. Here is a simple UNIT RIGHT TRIANGLE: BASE 1 UNIT; HEIGHT 1 UNIT (it looks distorted because the tools I must use to sketch it):

				*
                               /|
                              / |
                             *__*

In this i = 0; b = 3. Hence, A = 0 + 3/2 - 1 = 1/2 SQUARE UNITS. That agrees with the STANDARD FORMULA: A = 1/2 BASE x HEIGHT, where BASE and HEIGHT are both 1 UNIT LENGTH. Hence, A = 1/2 X 1 X 1 = 1/2 SQUARE UNIT.

For a RECTANGLE, A = BASE X HEIGHT. In that below, BASE IS 3 UNITS; HEIGHT IS 2 UNITS. So. A = 3 X 2 = 6 SQUARE UNITS. I'll draw a crude likeness of it and count the "points" and use the FORMULA:

                     *----*----*----*                         
                     |    |    |    |
                     *----*----*----*
                     |    |    |    |
                     *----*----*----*

Here, we have 2 INTERIOR POINTS (i = 2); and 10 BOUNDARY POINTS (b = 10). Then:A = 2 + 10/2 - 1 = 2 + 5 - 1 = 6 SQUARE UNITS, as desired.

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You now have all you need to make other geometric sketches on paper and determine their areas by this FORMULA.

As the TITLE indicates, these structures can be sketched by chalk on a tile floor or tiled wall. You can also build similar structures on a pegboard by putting pegs in the holes of the pegboard.