Example Question - polygon diagonals
Here are examples of questions we've helped users solve.
Polygon Diagonals and Triangles
The image shows a convex polygon, and the question asks, "How many triangles are formed by drawing all the diagonals from a single vertex?" To solve this, you can count the number of sides (vertices) of the polygon and then use the following formula to find the number of triangles formed: Number of triangles formed from one vertex = Number of vertices (n) - 2 However, I cannot visually determine the exact number of sides of the polygon from the image provided. To count the number of sides (vertices), you should start at one corner and move around the polygon, counting each corner until you end up at the starting corner again. If you can provide the number of sides, I can help you calculate the number of triangles.
Number of Triangles in Polygon
The image shows a convex polygon. To determine how many triangles are formed by drawing all the diagonals from a single vertex, we follow a general rule: For any polygon with n sides (an n-gon), the number of diagonals from a single vertex to all non-adjacent vertices is (n - 3), because you cannot draw a diagonal to the vertex itself or to the two adjacent vertices. In the image provided, the convex polygon appears to be a pentagon, which has 5 sides. So we apply the rule: Number of triangles formed = n - 3 Number of triangles formed = 5 - 3 = 2 Therefore, by drawing all the diagonals from one vertex in the pentagon, we would form 2 triangles.
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