https://file.aiquickdraw.com/mathbot/file/1727193958176qi6nbfk4.jpg

The image you've provided depicts a square that is subdivided into four regions, with the areas of three regions given as 20 cm², 32 cm², and 16 cm². The area of the fourth region is unknown and marked with a question mark.

To solve this:

### Step-by-Step Solution:

1. **Total Area of the Square**:
   Since all four regions are inside a square, the total area of the square is the sum of the areas of the four regions.

   Let the unknown area be denoted as \( A \). Thus:
   \[
   \text{Total Area of Square} = 20 \, \text{cm}^2 + 32 \, \text{cm}^2 + 16 \, \text{cm}^2 + A
   \]

2. **Assumption: Equal Side Length**:
   Notice that the square has equal sides marked by small tick marks, which suggests that the regions' boundaries are symmetric or related geometrically.

3. **Calculating the Total Area**:
   The total area of the square can be computed by adding the given areas:
   \[
   20 + 32 + 16 = 68 \, \text{cm}^2
   \]
   This means the total area of the square is 68 cm², including the unknown region.

4. **Finding the Unknown Area**:
   If the area of the entire square is 68 cm², the missing area (A) is:
   \[
   A = 68 - (20 + 32 + 16) = 68 - 68 = 0 \, \text{cm}^2
   \]

It appears that there was some misinterpretation in the total. However, based on the visual, the total area could be recalculated. Would you like to continue discussing this

What is the area of the fourth region in the square, given that the other regions have areas 20 cm², 32 cm², and 16 cm²?

Learn how to find the area of an unknown region within a square where three regions have known areas of 20 cm², 32 cm², and 16 cm². This problem involves basic geometry concepts and area calculations suitable for students in Grades 6-8.

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