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06 December, 2007

Sum of areas of 3 sectors of same radii

Aim:
By paper cutting and pasting, verify that the sum of areas of three sectors of same radius “r” formed at the vertices (as center) of any triangle is (Pi x r ^2)/2.

Material Required
Coloured paper, pair of scissors, glue, geometry box.

Procedure
Step 1 Draw an equilateral triangle ABC on a coloured paper and cut it.
Step 2 With suitable radius, draw three sectors on the three vertices.
Step 3 Cut the three sectors.
Step 4 Draw a straight line and place the three sector cut outs adjacent to each other on it.
Step 5 Write the observations.
Step 6 Repeat the activity for two more triangles other than equilateral triangle.
Step 7 Write the observations

Observations
1. When sector cut outs are placed on a straight line, they completely cover the straight angle. So their sum is 180 degrees.
2. The three sectors cut outs placed on a straight-line form a semicircle.
3. The area of semicircle is Pi x r^2 /2.

Cynthia D'Costa said...

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Regards
Ms. Cynthia D'Costa

Amit Gupta said...

THANKU RASHMIJI FOR A NICE HELP.

Amit Gupta said...

thanku