Which of the following is a true logical proposition?
A) A hexagon has nine diagonals
B) An octagon has eighteen diagonals
C) A pentagon has six diagonals
D) A triangle has two diagonals
E) A square has three diagonals
IMAT 2026 · Question 6
Q6 - Problem solving
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The correct answer is A) A hexagon has nine diagonals.
A diagonal joins two vertices of a polygon that are not next to each other. To count the diagonals of a polygon with n vertices, use:
Number of diagonals = n × (n − 3) ÷ 2
This formula works because each vertex can connect to n − 3 other vertices: we exclude the vertex itself and its two neighbours, since connections to neighbours are sides. We then divide by 2 because each diagonal has been counted from both ends.
A hexagon has 6 vertices, so it has 6 × (6 − 3) ÷ 2 = 9 diagonals.
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