A pentagon is a polygon made up of five sides and it has five corners. Its corners are joined in pairs.

A pentagon is a polygon made up of five sides and it has five corners. Its corners are joined in pairs.

Question 1.

A pentagon is a polygon made up of five sides, and it has five corners. Its corners are joined in pairs. Find the total number of line segments in the resulting shape. This number is a term of which sequence?

Solution:

On counting, the total number of sides = 10

It is a term of the sequence of triangular numbers.

Question 2.

In the sequence of snowflakes, find the number of line segments in the fifth snowflake.

Solution:

Here, the sequence formed is 3, 12, 48, 192, ...

i.e., 3, 3 × 4, 3 × 4 × 4, 3 × 4 × 4 × 4, 3 × 4 × 4 × 4 × 4, ...

So, required number of line segments = 3 × 4 × 4 × 4 × 4

= 3 × 256

= 768