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Question 3

Using diagonals from a common vertex, how many triangles could be formed from a decagon?

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To determine the number of triangles that can be formed from a decagon (a 10-sided polygon) using diagonals from a common vertex, start by selecting one vertex as the common point. From there, each of the remaining vertices can connect via a diagonal to create a triangle. In a decagon, you can connect to other vertices (where is the total number of sides), which gives you triangles per vertex. Since there are 10 vertices, the total number of triangles would be . However, each triangle gets counted three times (once at each vertex), so the final count is , but since we can only have whole triangles, it would be 23 triangles.

Additionally, a decagon is a great shape for creating various polygon-based projects, like designing a garden or a piece of art! Imagine using the diagonal triangles creatively to set up planting sections or painting designs. Such engaging activities allow you to visualize mathematical concepts in real-life applications, making learning a breeze and truly fun!