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Let A be a point inside a regular polygo...

Let A be a point inside a regular polygon of 10 sides. Let `p_(1), p_(2)...., p_(10)` be the distances of A from the sides of the polygon. If each side is of length 2 units, then find the value of `p_(1) + p_(2) + ...+ p_(10)`

Text Solution

Verified by Experts

The correct Answer is:
`(10)/(tan.(pi)/(10))`
In the figure, `h = (1)/(tan.(pi)/(10))`

Area of polygon `= 10 ((1)/(2) .2 (1)/(tan.(pi)/(10))) = (10)/(tan.(pi)/(10))`
Now, from point A inside polygon, draw perpendiculars from to the sides of polygon.
Then the area of polygon `= underset(i =1)overset(n)sum (1)/(2) .2p_(1) = (10)/(tan.(pi)/(10))`
`:. p_(1) + p_(2) + .. + p_(10) = (10)/(tan.(pi)/(10))`
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