motion2020 wrote:
How many diagonals are in a figure enclosed into the regular polygon with 26 sides, if the area of this enclosed figure is equal to exactly half of the area of the original regular polygon?
(A) 66
(B) 77
(C) 88
(D) 99
(E) 111
The formula for number of diagonals in a polygon = \(\frac{n(n-3)}{2}\)
Here the 26 sided polygon is cut into two halves, so the number of sides in one of the half = \(\frac{26}{2} + 1\)
So answer is \(\frac{14*11}{2} = 77\)
Answer is B) 77