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Find the number of diagonals of a polygon of 10 sides. |
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Answer» Assume that there are 10 points in a plane where no 3 of them are collinear which are the verticews of the given polygon, The number of different lines that can be formed by joining these 10 points is `.^(10)C_(2)`. We know in any polygon the lines joining non-adjacent vertices are called diagonals. Hence, the required number of diagonals=Number of lines formed -Number of sides of the polygon `=.^(10)C_(2)-10=35`. Using the formula, the number of diagonals in the above problem `=(10(10-3))/(2)=35`. |
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