How many diagonals does a dodecagon have?
Understand the Problem
The question is asking for the number of diagonals in a dodecagon, which is a polygon with 12 sides. To find the number of diagonals, we can use the formula D = n(n-3)/2, where n is the number of sides.
Answer
54
Answer for screen readers
The total number of diagonals in a dodecagon is $54$.
Steps to Solve
-
Identify the number of sides
Since we are dealing with a dodecagon, we identify that the number of sides, $n$, is 12. -
Substitute the value into the formula
Next, we substitute $n = 12$ into the formula for diagonals, which is given by:
$$ D = \frac{n(n-3)}{2} $$ -
Calculate n(n-3)
Now we calculate $n(n-3)$: $$ n(n-3) = 12(12-3) = 12 \times 9 = 108 $$ -
Divide by 2
Finally, we divide by 2 to find the number of diagonals:
$$ D = \frac{108}{2} = 54 $$
The total number of diagonals in a dodecagon is $54$.
More Information
A dodecagon has 12 sides, and the formula used to calculate the number of diagonals is applicable to any polygon. This formula allows us to efficiently determine the number of diagonals without having to list them all.
Tips
- Confusing the total number of sides with the number of diagonals. Remember, only some connections (non-adjacent sides) count as diagonals.
- Not applying the formula correctly. Make sure to subtract 3 from the number of sides before multiplying.
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