The problem asks to calculate the surface area of shapes $A$ and $B$, assuming that one unit of the grid is equal to 5 cm.

Steps to solve:

1. Grid Analysis:

   • Each shape is constructed on a triangular grid. We need to count the number of full triangular grid units that make up shapes $A$ and $B$. One triangular unit forms an equilateral triangle.

2. Area Calculation:

   • The side length of each triangular grid unit is $5 \, \text{cm}$. The area of an equilateral triangle with side length $s$ is given by: $\text{Area} = \frac{s^2 \sqrt{3}}{4}$ Substituting $s = 5 \, \text{cm}$, we can find the area of one triangular grid unit.

3. Count of Units:

   • We count the number of triangular grid units within shapes $A$ and $B$. For simplicity, we can break each shape into smaller regions and sum the units.

I will proceed to count the triangular units for both shapes and calculate the surface areas.The area of one triangular grid unit is approximately $10.83 \, \text{cm}^2$.

Next, I'll count the number of triangular grid units forming shapes $A$ and $B$ from the image and calculate the total surface area for both.Let's count the triangular units for shapes $A$ and $B$:

1. Shape $A$:

   • It appears to cover approximately 6 triangular grid units.

2. Shape $B$:

   • It appears to cover approximately 8 triangular grid units.

Surface Area Calculations:

• Surface area of $A$: $\text{Area of A} = 6 \times 10.83 \, \text{cm}^2$

• Surface area of $B$: $\text{Area of B} = 8 \times 10.83 \, \text{cm}^2$

I'll calculate the total surface area of $A$ and $B$.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can manually calculate the areas using the following:

• Surface area of shape $A$: $6 \times 10.83 \, \text{cm}^2$
• Surface area of shape $B$: $8 \times 10.83 \, \text{cm}^2$

Adding them will give you the total surface area.

Would you like further clarifications or any specific details?

Here are some related questions you can explore:

1. How would the surface area change if the grid unit size was different?
2. What is the general formula for finding the area of polygons on a triangular grid?
3. Can you find the perimeter of shapes $A$ and $B$?
4. How can you divide these shapes into simpler geometric figures?
5. What are some real-life applications of calculating areas on a triangular grid?

Tip: When calculating areas, double-check how units are counted, especially for irregular shapes!