To determine the number of pentagons that can be drawn by joining the vertices of a polygon with 10 sides, we need to understand the properties of a pentagon and the possible combinations of vertices.

Properties of a pentagon:
- A pentagon is a polygon with 5 sides.
- It has 5 vertices.

Possible combinations of vertices for a pentagon:
- To form a pentagon, we need to choose 5 vertices from the given polygon.
- The order of selecting the vertices does not matter, as the same set of vertices can be arranged in different orders to form different pentagons.

Now, let's calculate the number of pentagons:

Step 1: Choose 5 vertices from the polygon
- Since the polygon has 10 sides, we have 10 vertices.
- To choose 5 vertices, we can use the combination formula: C(n, r) = n! / (r!(n-r)!), where n is the total number of vertices and r is the number of vertices to be chosen.
- In this case, n = 10 and r = 5.
- Plugging in the values, we get C(10, 5) = 10! / (5!(10-5)!) = 10! / (5!5!) = (10*9*8*7*6) / (5*4*3*2*1) = 252.

Step 2: Count the number of distinct pentagons
- Since the order of selecting the vertices does not matter, some combinations may result in the same pentagon.
- To count the number of distinct pentagons, we need to divide the total number of combinations by the number of arrangements of the 5 selected vertices.
- The number of arrangements of 5 vertices is 5! = 5*4*3*2*1 = 120.
- Dividing the total number of combinations (252) by the number of arrangements (120), we get 252 / 120 = 2.1.

Therefore, the number of distinct pentagons that can be drawn by joining the vertices of a polygon with 10 sides is 2.1.

Since we cannot have a fraction of a pentagon, the correct answer is the closest whole number, which is 2. Hence, the correct answer is option 'B' (252).