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We are given a square that is 8 cm on each side, and two parts of it are shaded. We are asked to find the ratio of the shaded area to the unshaded area.

### Step 1: Calculate the total area of the square.
The side length of the square is 8 cm. The area \( A_{\text{total}} \) of the square is:
\[
A_{\text{total}} = 8 \times 8 = 64 \, \text{cm}^2
\]

### Step 2: Calculate the area of the unshaded region.
The unshaded region forms a smaller square with a side length of 4 cm (as shown in the image). The area \( A_{\text{unshaded}} \) of this smaller square is:
\[
A_{\text{unshaded}} = 4 \times 4 = 16 \, \text{cm}^2
\]

### Step 3: Calculate the area of the shaded region.
The shaded area is the total area minus the unshaded area:
\[
A_{\text{shaded}} = A_{\text{total}} - A_{\text{unshaded}} = 64 - 16 = 48 \, \text{cm}^2
\]

### Step 4: Find the ratio of the shaded area to the unshaded area.
The ratio of the shaded area to the unshaded area is:
\[
\text{Ratio} = \frac{A_{\text{shaded}}}{A_{\text{unshaded}}} = \frac{48}{16} = 3
\]

Thus, the ratio of the shaded area to the unshaded area is **3:1**.

Would you like further details on any step or additional questions?

Here are 5 related questions for practice:
1. If the side length of the square were doubled, how would the shaded and unshaded areas change?
2. What is the ratio of the perimeter of the unshaded square to the shaded region's total perimeter?
3. How would the ratio change if only one quadrant of the square were shaded?
4. Can you find the total length of the boundary between shaded and unshaded areas?
5. If a circle was inscribed in the unshaded region, what would its area be?

**Tip:** When working with area ratios, remember that both shaded and unshaded regions must add up to the total area.

Two parts of this square are shaded. The other two parts are unshaded. What is the ratio of the shaded area to the unshaded area? Give your answer in its simplest form.

Solve a geometry problem involving a square with two shaded parts. Learn how to calculate the area of shaded and unshaded regions and find the ratio of the shaded to unshaded area. This solution uses basic properties of squares and is suitable for Grade 6-8 students.

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