To solve this problem, let's start with a regular hexagon. A regular hexagon has six equal sides and six equal angles. Let's call this hexagon Hexagon 1.

Step 1: Draw Hexagon 1
Start by drawing a regular hexagon. Label the vertices as A, B, C, D, E, and F, in clockwise order.

Step 2: Find the Midpoints
Next, we need to find the midpoints of the sides of Hexagon 1. Let's call these midpoints M, N, O, P, Q, and R. To find the midpoints, draw a line segment connecting each pair of consecutive vertices of Hexagon 1. The midpoints will be the points where these line segments intersect.

Step 3: Join the Midpoints
Now, connect the midpoints M, N, O, P, Q, and R in order. This will form a new hexagon inside Hexagon 1. Let's call this hexagon Hexagon 2.

Step 4: Find the Area of Hexagon 1
The area of a regular hexagon can be found using the formula: Area = (3√3/2) * s^2, where s is the length of a side of the hexagon. Since all sides of Hexagon 1 are equal, we can simply write the area as A1.

Step 5: Find the Area of Hexagon 2
To find the area of Hexagon 2, we can divide it into six congruent equilateral triangles. The side length of each equilateral triangle is half the length of the side of Hexagon 1. Let's call this side length x. So, the area of each equilateral triangle is (sqrt(3)/4) * x^2. Since there are six equilateral triangles in Hexagon 2, the total area of Hexagon 2 can be written as 6 * (sqrt(3)/4) * x^2, which simplifies to (3√3/2) * x^2. We can write this area as A2.

Step 6: Find the Fraction of Area
To find the fraction of the area of Hexagon 1 that is occupied by Hexagon 2, we need to calculate the ratio of A2 to A1. Therefore, the fraction is A2/A1 = [(3√3/2) * x^2] / [(3√3/2) * s^2]. The (3√3/2) terms cancel out, leaving us with x^2/s^2. Since x is half the length of s, we can write x as s/2. Substituting this into the fraction, we get (s/2)^2 / s^2, which simplifies to 1/4.

Therefore, the fraction of the area of Hexagon 1 that is occupied by Hexagon 2 is 1/4.