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6:49 C .1ll 56؛ 75 deltamath.com Test Overview 3 \( \approx \) DeltaMath Previous Question Next Question Question 3 Using diagonals from a common vertex, how many triangles could be formed from a decagon? Answer \( : \because: \) Attempt 2 out of 5 \( \square \) Submit Answer Copyright ©2025 DeltaMath.com All Rights Reserved. Terms \& Policies

Ask by Robbins Ross. in the United States
Jan 16,2025

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You can form 21 triangles using diagonals from a common vertex in a decagon.

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Bonus Knowledge

Did you know that a decagon, which has ten sides, can create a whopping 35 triangles when you join its diagonals from a common vertex? This is because each set of diagonals from a vertex connects to all non-adjacent vertices. So, if you take one vertex and connect it to the other seven non-adjacent vertices, you can form triangles with each connection! For a fun tip, remember that the formula for calculating the number of triangles formed by drawing diagonals from one vertex in a polygon is \( n-2 \), where \( n \) is the number of sides in your polygon. So for our decagon, that would be \( 10-2 = 8 \), and since you’re connecting them from one vertex, you can then combine these to find all possible triangles, leading to that total of 35 mentioned earlier!

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