How many triangles?

First, any three points of the outer pentagon will give us a triangle ( 5C3); Next, we consider triangle that have 2 points outside and 1 point inside. With each point inside, there is one point outside that is not connected, and 2 pairs of point that in a line, leaving 4C2 - 2 = 4 options; and there are 5 points inside (5x4) Third, there are only 5 triangles with 2 points inside and 1 point outside, since 2 points inside must be next to together to be connected, and each pair has only 1 point outside that make them a triangle (5) There is no 3 points inside that all connected together. Hence, the answer is 5C3 + 5x4 + 5 = 35

Firstly there are 10 small outer triangles around the edge of the pentagon.

Secondly there are 5 large triangles given by any 2 adjacent points on the outer pentagon and the point on the opposite side.

Inside each of these 5 triangles there are 4 more triangles giving us the total of: $10 + 5 + (5 \times 4) = 35$

5 main triangles in the pentagon , each gives 7 so 5 * 7 gives 35

With each side of pentagon we are getting 4 triangles. So for 5 sides we r getting 5*4= 20 triangles. Taking 2 adjacent sides we are getting 5C2 =10 triangles. Lastly, we are getting 5 triangles from each vertices. Total no of triangles= 20+10+5=35

on each vertex there are 7 triangles :. there are 7times5=35

Single triangle based are 10 ( at each vertex ), double triangle based are 10 ( at each vertex ) , triple triangle based are 5 ( at each vertex ) center pentagon+2 triangle based are 5 center pentagon+3 triangle based are 5

from each base of pentagon there are 3 triangles and 5 are inside it