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Math Labs with Activity - Find the Area of Geometric Figures by Using a Geoboard

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Math Labs with Activity – Find the Area of Geometric Figures by Using a Geoboard

OBJECTIVE

To find the area of various geometric figures by using a geoboard.

Materials Required

  1. A playboard
  2. A sheet of coloured glazed paper
  3. A geometry box
  4. Nails
  5. A hammer
  6. A few rubber bands
  7. A tube of glue

Procedure
Making a Geoboard Paste the coloured glazed paper on the plyboard.
Mark an array of 20 x 20 dots at equal distances of 1 cm each. Fix nails at each one of the dots. We thus get a geoboard.
Using the Geoboard
Step 1: Make different types of geometric figures using rubber bands as shown in Figure 23.1.
Math Labs with Activity - Find the Area of Geometric Figures by Using a Geoboard 1
Step 2: For each geometric figure count the number of unit squares involved. The area of each complete square is counted as 1 cm² and that of each incomplete square is taken to be ½ cm².
Step 3: The area of each geometric figure is thus calculated and verified by using the formula derived by geometry.

Observations and Calculations

  1. Area of the Square
    Number of complete unit squares = 9.
    Number of incomplete unit squares = 0.
    ∴ area of the given square ={(9 x 1)+(0 x ½)}= 9 cm².
    Verification: Each side of the square = 3 cm. (From Figure 25.1.) area (by formula) = 3² =9 cm².
  2. Area of the Rectangle
    Number of complete unit squares = 24.
    Number of incomplete unit squares = 0.
    area of the given rectangle = {(24 x 1)+(0 x ½)}= 24 cm².
    Verification: Length = 6 cm and breadth = 4 cm. (From Figure 25.1.) ,
    ∴ area of the rectangle (by formula) = l x b = 6 x 4 = 24 cm².
  3. Area of the Triangle
    Number of complete unit squares = 9.
    Number of incomplete unit squares = 10.
    ∴ area of the given triangle = {(9 x 1)+(10 x ½)} = (9+5) = 14 cm².
    Verification: Base = 7 cm and height = 4 cm. (From Figure 25.1.)
    ∴ area of the triangle (by formula) =½ x b x h = ½ x 7 x 4 = 14 cm².
  4. Area of the Parallelogram
    Number of complete unit squares = 12.
    ∴ area of the given parallelogram =  {(12 x 1)+(12 x ½)} = (12+6) = 18 cm².
    Number of incomplete unit squares = 12.
    Verification: Base = 6 cm and height = 3 cm. (From Figure 25.1.)
    ∴ area of the given parallelogram (by formula)
    =b x h = 6 x 3= 18 cm².
  5. Area of the Trapezium
    Number of complete unit squares = 19.
    Number of incomplete unit squares = 10.
    ∴ area of the given trapezium = {(19 x 1)+(10 x ½)} = (19 + 5) = 24 cm².
    Verification: The parallel sides of the trapezium are 5 cm and 11 cm and its height is 3 cm. (From Figure 25.1.)
    ∴ area of the given trapezium (by formula)
    = ½ x (sum of the parallel sides) x height
    = ½ x (5 +11) x 3 = ½ x 16 x 3 = 24 cm².

Result
The area of any geometric figure estimated by using a geoboard has been verified by using the respective geometric formula.

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