In the diagram, all triangles are equilateral. The total number of equilateral triangles of any size is
(A) 18
(D) 26
(B) 20
(E) 28
(C) 24

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-135.jpg?height=380&width=225&top_left_y=569&top_left_x=1424)
In the diagram, all triangles are equilateral. The total number of equilateral triangles of any size is
(A) 18
(D) 26
(B) 20
(C) 24
(E) 28

![](https://cdn.mathpix.com/cropped/2024_04_20_faa9db06d997f2a5b9b1g-220.jpg?height=412&width=250&top_left_y=1390&top_left_x=1512)

## Solution

From the diagram, if we start by counting just the small triangles we would achieve a total of 18 triangles. If we count triangles that have a side length of 2, there would be 6 including 3 in each of the top and bottom halves. However, there are an additional 2 that are overlapping the two halves. If we count the 2 additional triangles of side length 3 , we would have a total of 28. ANSWER: (E)