The problem asks to find the perimeter of a compound shape made up of two squares with a total area of 80 cm². The dimensions provided in the image are:

• One side of the vertical square: 8 cm
• The side length of the square at the top-right is given as 10 cm.

Step 1: Verify the area of the squares

The total area is 80 cm², which means the combined area of the two squares must equal this. Each square's area is found using the formula for the area of a square: $\text{Area} = \text{side}^2$.

• For the first square (with a side of 8 cm), the area is $8^2 = 64 \, \text{cm}^2$.
• For the second square (with a side of 10 cm), the area is $10^2 = 100 \, \text{cm}^2$.

However, this leads to a total of $64 \, \text{cm}^2 + 100 \, \text{cm}^2 = 164 \, \text{cm}^2$, which does not match the given area of 80 cm².

Thus, the correct interpretation is that these squares overlap partially and therefore need careful calculation of their contributing areas. We can proceed by calculating the perimeter with adjustments based on shared sides. Let me clarify the correct process for finding the perimeter.Let's reconsider the compound shape based on the diagram:

• Square 1 (on the left) has a side length of 8 cm.
• Square 2 (on the right) has a side length of 10 cm.
• The total area is given as 80 cm², and we need to determine how the shapes fit together to meet this area.

Step 1: Understanding the dimensions and arrangement

The compound shape consists of two squares, and it appears that part of one square overlaps with the other.

• Since the area is given as 80 cm², we can set the area of Square 1 (8 cm by 8 cm) as 64 cm². To achieve the total area of 80 cm², Square 2's area must contribute an additional 16 cm².
• We can deduce that Square 2 extends beyond the edge of Square 1, and part of it overlaps to form this shape.

Step 2: Determine the perimeter

To calculate the perimeter, we need to add the lengths of all the outer edges of the compound shape. From the diagram:

• The left vertical side of the shape is 8 cm (side of the first square).
• The bottom horizontal side is 10 cm (side of the second square).
• The right vertical side is 8 cm.
• The top horizontal side is 10 cm, but part of it overlaps with the first square.

We can now add the lengths of these visible edges to find the perimeter of the compound shape.

Would you like me to go over the specific perimeter calculation steps, or is there something specific you'd like me to clarify further?