# Count the Number of Triangles in Given Figure.

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The total number of triangles in the given figure is 27. The number of triangles can be obtained easily by using a simple formula which is total number of triangles = [n(n+2)(2n+1)] / 8 where ‘n’ is the number of triangles in sides.

In the given figure, we can see that the number of triangles on each side is 4.

So, n = 4

Now, the formula to find total number of triangles = [n(n+2)(2n+1)] / 8 (equation 1)

On putting the value of ‘n’ in equation 1, we will get:

total number of triangles = [4(4+2)(2 x 4 + 1)] / 8

total number of triangles = [(16+8)(8 + 1)] / 8

total number of triangles = (24)(9)/ 8

total number of triangles = 3 x 9

Therefore, total number of triangles = 27.

Table of content

## Number of Triangles in Given Figure

As discussed above, there are a total of 27 triangles in the given figure. Three edges and three vertices make up a triangle, which is a polygon. It is among the fundamental shapes in geometry. Triangle ABC refers to a triangle with the vertices A, B, and C.

In Euclidean geometry, any 3 points that are not collinear determine a singular triangle and a singular plane at the same time. The most significant characteristic of a triangle is that the sum of its internal angles equals 180 degrees. This is known as the angle sum property of triangles.

## Types of Triangles

A triangle is a 3-sided polygon that is also referred to as the trigon. There are three sides to every triangle as well as three angles. Triangles are classified into three types based on their side lengths: scalene, isosceles, and equilateral.

• A scalene triangle is a triangle with three sides that are various sizes and angles that are all of various dimensions. The sum of all interior angles, however, always remains equal to 180 degrees.
• Any triangle with (at least) two equal sides is said to be isosceles. The two angles of this triangle are also equal. Therefore, an isosceles triangle has two equal sides as well as two equal angles.
• A triangle is said to be equilateral if each of its three sides is the same length.

Summary:

## Count the Number of Triangles in Given Figure.

Total 27 triangles are there in the given figure. The number of triangles can be easily determined by using the formula [n(n+2)(2n+1)] / 8 where ‘n’ is the number of triangles on each side. A triangle is a polygon having three sides and three angles.

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