Math Problem Statement

A pentagon can be divided into how many triangles by drawing all of the diagonals from one vertex?

Solution

To determine how many triangles a pentagon can be divided into by drawing all diagonals from one vertex, we can use a formula for any polygon. The number of triangles formed is given by:

Number of triangles=n2\text{Number of triangles} = n - 2

where nn is the number of sides of the polygon.

In this case, a pentagon has 5 sides (n=5n = 5):

Number of triangles=52=3\text{Number of triangles} = 5 - 2 = 3

Thus, the correct answer is:

A. 3

Would you like more details or have any questions?

Here are 5 related questions for you to explore:

  1. How many triangles can be formed from a vertex in a hexagon?
  2. What is the relationship between the number of sides in a polygon and the number of diagonals?
  3. How do you calculate the interior angle sum of a polygon?
  4. How do you determine the number of diagonals in a polygon?
  5. How many diagonals are there in a regular octagon?

Tip: For any nn-sided polygon, the formula to find the number of triangles formed from one vertex is n2n - 2.

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Math Problem Analysis

Mathematical Concepts

Polygon Geometry
Diagonals
Triangles in Polygons

Formulas

Number of triangles = n - 2

Theorems

Basic Polygon Triangle Division

Suitable Grade Level

Grades 6-8