Find the number of triangles in the given figure? <img src="/api/images/count-triangles-in-star-figure.png" alt="Geometric puzzle image of a five-pointed star formed by overlapping straight lines, designed to count all triangles formed within and around the star pattern" width="300" height="200" loading="lazy" decoding="async" class="rounded border border-gray-300 mx-auto my-4" />

Question: Find the number of triangles in the given figure.

Step 1: Understand the structure of the figure

The figure is a classic five-pointed star, known as a pentagram. It is formed by extending the sides of a regular pentagon so that they intersect.

Step 2: Visual decomposition of the triangles

We will count all the triangles — both visible and hidden — formed by the intersecting lines.

• 5 outer triangles – These are the large isosceles triangles pointing out from the center, formed by the star's arms.
• 5 inner triangles – These are formed inside the star where the arms intersect with each other, creating small overlapping triangular regions.

Step 3: Total count

Adding both types of triangles:

• Outer triangles: 5
• Inner triangles: 5

Total triangles = 5 + 5 = 10

Final Answer: 10 triangles