The base of the prism is a rectangle with sides 13 m and 5 m in length. Find the lateral surface and surface area of the given prism.

L = 13 m.

W = 5 m.
h = 5 m.(Assumed).

Al = (W*h)*2 + (L*h)*2.
Al = (5*5)*2 + (13*5)*2 = 180 m^2. =
Lateral area.

As = (W*h)*2 + (L*h)*2 +(L*W)*2. =
Surface area.

Also: As = Al + (L*W)*2.

To find the lateral surface area of the prism, we need to calculate the combined area of all the vertical faces. The lateral surface area can be found by multiplying the perimeter of the base by the height of the prism.

1. Calculate the perimeter of the base:
The perimeter of a rectangle is given by the formula: P = 2(length + width)
Given that the length (L) of the rectangle is 13 m and the width (W) is 5 m, we can substitute the values into the formula:
Perimeter (P) = 2(13 m + 5 m) = 2(18 m) = 36 m

2. Calculate the height (H) of the prism:
The height of the prism refers to the distance between the bases.
Since the problem does not provide a value for the height, we cannot calculate the lateral surface area. Please provide the height of the prism for a more accurate answer.

Assuming you have the height of the prism, we can move on to calculating the surface area of the entire prism, which includes the base and the lateral faces.

3. Calculate the area of the base:
The area of a rectangle is given by the formula: A = length * width
Given the length (L) of the rectangle is 13 m and the width (W) is 5 m, we can substitute the values into the formula:
Area of the base = 13 m * 5 m = 65 m^2

4. Calculate the lateral surface area:
The lateral surface area, as mentioned earlier, is the combined area of all the vertical faces of the prism. Since we do not have the height, we cannot calculate the lateral surface area accurately.

However, assuming you have the height, the formula to calculate the lateral surface area is:
Lateral Surface Area = Perimeter of base * Height

5. Calculate the total surface area:
The total surface area refers to the sum of the base area and the lateral surface area.
Total Surface Area = Lateral Surface Area + 2 * Base Area

Once you provide the height of the prism, I can help you with the accurate calculation of the lateral surface area and the total surface area.