To verify experimentally that
the parallelograms on the same base and between same parallels are equal in
area.
MATERIAL REQUIRED
A piece of plywood, two wooden strips, nails, elastic
strings, graph paper.
METHOD OF CONSTRUCTION
1.
Take a rectangular piece of plywood
of convenient size and paste a graph paper on it.
2. Fix two
horizontal wooden strips on it parallel to each other [see Fig. 1].
Fig. 1
3. Fix two
nails A1 and A2 on one of
the strips [see Fig. 1].
4. Fix nails at
equal distances on the other strip as shown in the figure.
DEMONSTRATION
1.
Put a string along A1,
A2, B8,
B2 which forms a parallelogram A1A2B8B2.
By counting number of squares, find the area of this parallelogram.
2.
Keeping same base A1A2,
make another parallelogram A1A2B9B3
and find the area of this parallelogram by counting the squares.
3. Area of
parallelogram in Step 1 = Area of parallelogram in Step 2.
OBSERVATION
Number
of squares in 1st parallelogram = --------------.
Number
of squares in 2nd parallelogram = -------------------.
Number
of squares in 1st parallelogram = Number of squares in 2nd parallelogram.
Area
of 1st parallelogram = --------- of 2nd parallelogram
APPLICATION
This result helps in solving various geometrical problems.
It also helps in deriving the formula for the area of a paralleogram.
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