The question provided shows a square divided into two rectangles. The total perimeter of both rectangles is given as 30 units, and we are asked to find the area of the original square.

Step-by-step solution:

1. Understanding the situation:

   • You have a square, and it's divided into two equal rectangular parts by a horizontal line.
   • Let's assume the side length of the original square is $s$.
   • The two rectangles created will have dimensions $s \times \frac{s}{2}$, as each rectangle will have half the height of the square.

2. Perimeter of one rectangle: The perimeter $P$ of one rectangle is given by the formula: $P = 2 \times (\text{length} + \text{width})$ For one rectangle with dimensions $s \times \frac{s}{2}$: $P = 2 \times \left( s + \frac{s}{2} \right) = 2 \times \frac{3s}{2} = 3s$

3. Total perimeter: Since the problem gives the total perimeter of both rectangles as 30, we can write the equation: $2 \times (3s) = 30$ Solving for $s$: $6s = 30$ $s = 5$

4. Area of the square: The area $A$ of the square is given by: $A = s^2 = 5^2 = 25$

Thus, the area of the original square is 25 square units.

Would you like further details or clarification? Here are 5 follow-up questions for better understanding:

1. What is the relationship between perimeter and area for basic shapes like squares and rectangles?
2. How does dividing a shape affect its perimeter and area?
3. Can the perimeter of two different shapes sum up to the same value, but their areas differ?
4. What other methods could be used to solve for the area of the square?
5. How can this problem be adapted for different types of shapes or dimensions?

Tip: When dealing with perimeter and area problems, always keep track of how dividing or combining shapes affects these two properties.