Solution:

There are 20 triangles.

Solution:

47

Explanation:
At first look, it seems pretty easy but on the contrary, it is pretty tricky a question. So let us simplify it by dividing the triangle into three equal triangles (the triangles so formed if outer side is connected to the center of the circle) and then count the number of triangles in each part by taking two or more parts together.

First, let us take the triangles in one part. There are 4 non-overlapping and 3 overlapping triangles.
4 + 3 = 7
7 * 3 = 21

Next, if we take number of triangles by taking two parts together, there are 8 in total.
8 * 3 = 24

Lastly, the number of triangles if all three parts are taken together, there are a total of 2.

21 + 24 + 2 = 47.

Solution:

38

Explanation:
The total number of triangles are 8.

Let us divide the triangles in three categories: small, medium and large.

If we start with the small triangles, you can count a total of 24 triangles. 12 triangles (3 + 4 + 3 + 2) are upward facing and 12 are downward facing.

Next, we count the medium sized triangles. You can find a total of 12 triangles. 6 triangles (3 + 2 + 1) are facing upwards and 6 are facing downwards.

Lastly, if you calculate the large triangles, they are only two. One is upward facing and one is facing downward.

24 + 12 + 2 = 38.

Solution:

35

Solution:

64

Solution:

8

Solution:

40 triangles

16 + (8x2) + (4x2) + (1x2) + (1x2)

Solution:

20 Triangles

Explanation:
Let us consider the smallest side of the triangle as 1 cm.
Now count and you will find out that we have 1 + 5 + 5 + 1 = 12 triangles with the side 1 cm.
Number of triangles with side 2 cm = 1 + 2 (triangles facing upwards) + 1 + 2 (triangles facing downwards = 6 triangles
Number of triangles with side 3 cm = 2 (a triangle facing upwards + a triangle facing downwards)

Summing them up, we have 20 triangles in total.

Solution:

13