find the number of diagonals for a decagon
Answers
Answer:
35 diagonals
Step-by-step explanation:
A decagon has 10 vertices, by definition (deka is Greek for ‘ten’).
Every vertex can be joined to the other 9 vertices. Two of the 9 resulting straight line segments, viz. the ones joining that vertex to the next vertex on the left and on the right, are sides of the decagon. The other 7 are diagonals.
Are there, then, 10 times 7 = 70 diagonals? No, because each diagonal has been counted twice (once starting with one of its ends and one starting with the other.) There are therefore ½ of 70, i.e. 35 diagonals in a decagon.
Generally, a polygon with n sides has ½n(n-3) diagonals: none for a triangle, 2 for a quadrilateral, 5 for a pentagon, 9 for a hexagon etc.
Answer:
There are 10 vertices in a decagon. Now by joining two vertices, we get a side of decagon or a diagonal. Hence, the number of the line segment by joining of vertices of decagon = number of ways taking 2 points out of 10 points = 10C2 = (10(10 - ))/2! Now, there are 10 sides of decagon in 10C2 line segment ∴ Required number of diagonals
Step-by-step explanation:
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