To solve this problem, we need to calculate the surface areas of the regions labeled "A" and "B" in the grid shown in the image. The grid consists of triangular units, and we know that each unit of the grid represents an area of $5 \, \text{cm}^2$.

Steps to Calculate the Surface Areas:

1. Identify the number of grid units: Count the number of full triangular units that make up each region (A and B). Each of these units has a surface area of $5 \, \text{cm}^2$.

2. Calculate the total area: Multiply the number of triangular units in each region by the area of one unit ($5 \, \text{cm}^2$) to find the total surface area for both regions A and B.

Let me examine the image to determine the number of triangular units for regions A and B. After counting, I'll provide the calculations.

Counting Triangular Units in Regions A and B:

• Region A: Let's count the full and half triangles within region A.
• Region B: Similarly, count the full and half triangles within region B.

I'll do the counting now and perform the calculations for the surface areas.### Counting the Triangular Units in Regions A and B:

1. Region A:

   • Region A appears to be comprised of 7 full triangular units.

2. Region B:

   • Region B appears to be comprised of 5 full triangular units.

Calculating the Surface Areas:

Each triangular unit is equal to $5 \, \text{cm}^2$.

• Surface area of Region A: $\text{Area of A} = 7 \times 5 = 35 \, \text{cm}^2$

• Surface area of Region B: $\text{Area of B} = 5 \times 5 = 25 \, \text{cm}^2$

Conclusion:

• The surface area of Region A is 35 cm².
• The surface area of Region B is 25 cm².

Would you like any more details on this solution, or do you have any further questions?

Related Questions to Explore:

1. How do you find the area of a shape using a different type of grid?
2. What would the surface area be if each unit was 6 cm² instead of 5 cm²?
3. Can you calculate the perimeter of regions A and B?
4. How would the area change if the grid were not equilateral triangles but squares?
5. How can we approximate areas for irregular shapes on a grid?

Tip: Always double-check the unit area given for each grid cell when solving similar problems.