Finding Area on a Geoboard

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Finding Area on a Geoboard

• By Laurie Matecki

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What is Area?
Area is the amount of units an object takes up.
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What is a Geoboard?
This is a type of board with pegs/nails on it,
size and materials may vary.
Example
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Materials Needed for a Geoboard
Well, first of all if you dont have one, you
can make one with a 5 x 5 piece of wood and 25
nails. However, once you have a geoboard, all
you need is some rubber bands of various sizes.
For more thorough instructions and a pattern for
making geoboards click here.
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How to Find Area on a Geoboard
Therefore,
When finding area, consider each little square,
one unit.
1 2 3 4
5 6 7 8
is equal to one unit.
9 10 11 12
On this particular board, there are 16 possible
units.
13 14 15 16
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How to Find Area on a Geoboard
Cont
There are three main ways of finding area on a
geoboard

• Fill and count

• Halving

• Surround and uncount

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Fill and Count
In this method, one would fill the area inside
the object and count how many squares were
included inside the object.

• If you had a square, you would fill in the square
  to see how many smaller squares fit.

• As you can see, 4 smaller squares fit inside this
  big square.

1
2
3
4
4
So what is its area?
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Halving
In this method, diagonals must be present. One
counts the number of squares a diagonal is
passing through, and then divides that by two,
halving it.
Or, when a diagonal divides two area units,
When you have a triangle whose diagonal goes
through one unit,
the area of the triangle is equal to area one
because 2 / 2 1.
the area of the triangle is equal to ½ unit.
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Halving
In this method, diagonals must be present. One
counts the number of squares a diagonal is
passing through, and then divides that by two,
halving it.
With this triangle, the total area would be 1½
units because 3/2 1 ½ .
Another example would be when you have a diagonal
passing through three area units.
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Surround and Uncount
In this method, one would surround the entire
shape and find that whole area. Then one would
count the area that is NOT included within the
shape, and subtract it from the whole area.
However, 4 of the squares are only using half of
the unit, so therefore 2 units are outside of the
hexagon.
If you had a hexagon,
you would surround the entire shape,
1
2
3
and then count how many squares are included in
that area.
4
5
6
So, 6 2 4
As you can see, six units are in the whole area.
Therefore, the area of the hexagon is 4.
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Surround and Uncount
In this method, one would surround the entire
shape and find that whole area. Then one would
count the area that is NOT included within the
shape, and subtract it from the whole area.
surrounding the entire area works better.
Another example of this method would be when you
have a triangle such as this one.
Look at this triangle and tell me what you think
the area is.
Since you cant easily fill this triangle,
If you said 2 ½ , YOURE RIGHT!
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Surround and Uncount
In this method, one would surround the entire
shape and find that whole area. Then one would
count the area that is NOT included within the
shape, and subtract it from the whole area.
How did I get 2 ½?
Then you uncount the units outside of the
triangle using your halving skills.
Well, first you count that there are a total of 9
units within this square surrounding the triangle.
1 2 3
3
4 5 6
3
Therefore, 9 3 3 ½ 2 ½
7 8 9
½
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For More Information
Here are some web sites that might be helpful for
practice, or for understanding the area of
geoboards better.

• Area on the Geoboard

• A New Algebra Area on Geoboards

• Geoboard

• Investigating the Concept of Triangle and the
  Properties of Polygons Making Triangles

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Click Here for an Interactive Geoboard to Test
Your New Skills
This concludes my instructions on how to find
area using a geoboard.