Let's start by drawing the described net. We are told that the given net corresponds to a pentagonal pyramid.
The pentagon contributes five segments. Moreover, there are two extra segments for each of the five vertices of the pentagon. These are the segments that come together to create the triangles. The number of segments of the net is the sum of these. Therefore, the number of segments is 5+10= 15.
Note that the net has one pentagonal region and five triangular regions. therefore, the number of regions is the sum of these.
1+ 5= 6
Finally, let's recall Euler's Formula for 2-D figures.
F+V=E+1
Here, F is the number of regions, V the number of vertices, and E the number of segments of the net. To find the number of vertices of our net, we can substitute F= 6, E= 15 in the above and formula, and solve for V.
