**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**

- A playboard
- A sheet of coloured glazed paper
- A geometry box
- Nails
- A hammer
- A few rubber bands
- 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.

**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**

**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.**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.**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.**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.**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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