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We are given that \( ABCD \) is a square with a side length of \( 20 \, \text{m} \). The points \( P \), \( Q \), \( R \), and \( S \) are midpoints of the sides of the square, and joining the lines \( PC \), \( QD \), \( RA \), and \( SB \) forms the quadrilateral \( EFGH \).

### Key Observations:
- Since \( P \), \( Q \), \( R \), and \( S \) are midpoints of the sides, the lines \( PC \), \( QD \), \( RA \), and \( SB \) divide the square into several smaller regions.
- \( EFGH \) is formed inside the square by connecting those lines.

### Approach:
The diagonals of the square divide it symmetrically, and since the points are midpoints, it’s a well-known result in geometry that the area of the inner quadrilateral \( EFGH \), when such lines are drawn, is always **half** of the area of the original square.

### Calculation:
1. The area of the original square \( ABCD \) is:
   \[
   \text{Area of } ABCD = 20^2 = 400 \, \text{m}^2
   \]

2. The area of the quadrilateral \( EFGH \) is half of this:
   \[
   \text{Area of } EFGH = \frac{400}{2} = 200 \, \text{m}^2
   \]

Thus, the area of the quadrilateral \( EFGH \) is \( 200 \, \text{m}^2 \).

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Would you like a more detailed explanation on how this geometric result is derived? Feel free to ask!

### Related Questions:
1. How can the area of a triangle inside a square be calculated?
2. What are the properties of midpoints in a quadrilateral?
3. What is the significance of the diagonals in determining areas within a square?
4. Can we generalize this result to other types of polygons?
5. How would the area change if the square's side length is different?

**Tip:** When dealing with geometric problems involving midpoints, consider symmetry and how lines divide areas, as these often lead to elegant solutions!

ABCD is a square of side length 20 m. P, Q, R, and S are midpoints of sides of ABCD as shown. Joining PC, QD, RA, and SB, we get a new quadrilateral EFGH. Find the area of quadrilateral EFGH.

This problem involves finding the area of an inner quadrilateral (EFGH) formed by midpoints of the sides of a square with side length 20 meters. Using the midpoint theorem and symmetry properties, we calculate that the area of EFGH is 200 m².

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