Use formulas to find the lateral area and surface area of the given prism. The base of the prism is the rectangle with sides of length 13m and 5m. Show your answer to the nearest whole number.
You also need the height of the prism to find the lateral and surface areas. This site shows you how.
http://math.com/tables/geometry/surfareas.htm
To find the lateral area of the prism, we need to find the perimeter of the base and then multiply it by the height of the prism.
The perimeter of a rectangle is given by the formula: P = 2l + 2w, where l is the length and w is the width.
For the given rectangle with sides of length 13m and 5m, the perimeter would be:
P = 2(13m) + 2(5m)
P = 26m + 10m
P = 36m
Now, to find the lateral area, we multiply the perimeter by the height of the prism. Let's assume the height of the prism is h meters.
Lateral area = P * h
Lateral area = 36m * h
Next, to find the surface area of the prism, we need to find the sum of the lateral area and the areas of the two base rectangles.
The area of a rectangle is given by the formula: A = l * w, where l is the length and w is the width.
For the given rectangle with sides of length 13m and 5m, the area would be:
A = 13m * 5m
A = 65m^2
Now, to find the surface area, we sum the lateral area and the areas of the two base rectangles:
Surface area = Lateral area + 2 * A
Surface area = 36m * h + 2 * 65m^2
Please provide the height of the prism in order to calculate the final values.
To find the lateral area and surface area of the given prism, we need to use the following formulas:
1. Lateral area of a prism = perimeter of the base × height
2. Surface area of a prism = 2 × base area + lateral area
Step 1: Find the perimeter of the base.
The base of the prism is a rectangle with sides of length 13m and 5m. The formula for the perimeter of a rectangle is P = 2l + 2w, where l is the length and w is the width.
Perimeter = 2(13m) + 2(5m) = 26m + 10m = 36m
Step 2: Find the height.
The height of the prism is not given. Since the problem doesn't provide any specific information about the height, we can't calculate it. Without the height, we won't be able to find the exact values for the lateral area and surface area.
However, assuming the height is given or you have a known value for it, you can proceed with the calculations.
Step 3: Calculate the lateral area.
If the value of the height is known, we can use the formula for the lateral area of a prism: Lateral area = Perimeter of the base × Height.
For example, if the height is 7m:
Lateral area = 36m × 7m = 252m²
Step 4: Calculate the surface area.
Using the formula for the surface area of a prism: Surface area = 2 × base area + Lateral area.
First, calculate the base area of the rectangle.
Base area = length × width = 13m × 5m = 65m²
Then, plug in the values:
Surface area = 2 × 65m² + 252m² = 130m² + 252m² = 382m²
Therefore, to the nearest whole number, the lateral area of the prism is 252m², and the surface area is 382m².