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Find the number of quadrilaterals that can be made using the vertices of a polygon of 10 sides as their vertices and having exactly 2 common sides with the polygon>

Find the number of quadrilaterals that can be made using the vertices of a polygon of 10 sides as their vertices and having exactly 2 common sides with the polygon>

Grade:11

1 Answers

Ravi
askIITians Faculty 69 Points
6 years ago
Consider that to form a quadrilateral, 4 sides are needed of which only 2 need to be common with the decagon. So, selecting the first side can be done in 10 ways. The second side has to be selected from the 9 barring the 2 adjacent sides of the first side(so as not to include any more sides of the polygon in the quadrilateral formation). So 7 ways. As the last 2 sides will be formed by joining the end points of the selected sides(not being common to the polygon), so that will give the maximum no. of quadrilaterals that can be formed. But this no. will have twice the no. of unique quadrilaterals that can be formed. Apply the conditions to evaluate your answer.

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