Bishop's Paradise
Weekly Problem 37 - 2013
Which of the statements about diagonals of polygons is false?
Which of the statements about diagonals of polygons is false?
Which of the following statements is false?
A An octagon has $20$ diagonals
B A hexagon has $9$ diagonals
C A hexagon has $4$ more diagonals than a pentagon
D A pentagon has the same number of diagonals as it has sides
E A quadrilateral has twice as many diagonals as it has sides
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Image
![Bishop's Paradise Bishop's Paradise](/sites/default/files/styles/large/public/thumbnails/content-id-2903-Weekly%2525202013%252520-%25252037%252520Solution%2525202.png?itok=Jr4Jzr3f)
This can be used to show that A to D are all correct. A quadrilateral has half as many diagonals as it has sides, not twice as many, so statement E is false.
Image
![Bishop's Paradise Bishop's Paradise](/sites/default/files/styles/large/public/thumbnails/content-id-2903-Weekly%2525202013%252520-%25252037%252520Solution.png?itok=ErLyO6GR)