how many triangles are there

June 27, 2026

There isn’t a single fixed number of triangles in “geometry”; it depends on what exactly you’re asking about.

Below are the main ways people mean “how many triangles are there?” and what the answers look like.

1. As a basic shape in geometry

In pure geometry, a triangle is simply a polygon with three sides, three vertices, and three interior angles whose measures always add up to 180 degrees.

There is no limit to how many different triangles exist:
- Side lengths can vary continuously.
- Angles can vary continuously as long as they sum to 180 degrees.
So in this sense, there are infinitely many possible triangles.

2. Types of triangles (a finite list)

If you mean “how many types of triangles are there?”, then we usually talk about classifications by sides and by angles.

By side lengths:

Equilateral (three equal sides).
Isosceles (two equal sides).
Scalene (all sides different).

By interior angles:

Acute (all angles < 90°).
Right (one angle = 90°).
Obtuse (one angle > 90°).

So in common school-level classification, six named types are listed (3 by sides, 3 by angles), and some sources discuss combinations which give several more specific categories.

3. Those viral “count the triangles” puzzles

Often, the question “how many triangles are there?” is about a specific picture that hides lots of overlapping triangles. In that case, the answer depends completely on the exact diagram, not on geometry in general.

Example:

In one popular triangular grid with four small triangles along the base, you can systematically count all sizes and orientations and find 27 triangles in total.

In another well-known puzzle image discussed on forums, a careful combinatorial argument shows there are 18 triangles in that particular arrangement.

Because there are many different puzzle images, each one has its own correct count.

4. How to answer this in a post

If you’re writing a post with the title “how many triangles are there” and a side heading “Quick Scoop,” a concise claim that fits most readers’ curiosity is:

In pure geometry, there are infinitely many possible triangles, but in popular puzzle diagrams the exact number varies by picture (often 18, 27, or another specific count).

You can then briefly explain the three interpretations above so readers coming from “latest news,” “forum discussion,” or “trending topic” angles all get what they were looking for.

TL;DR:

As a shape in geometry: infinitely many triangles.

As named types: six basic types (by sides and by angles).

In a specific puzzle picture: the number is finite and diagram‑dependent (e.g., 18 or 27 in famous examples).

Information gathered from public forums or data available on the internet and portrayed here.