8.9m
47m
8m
4m
Use the formulas to find the lateral area and surface area of the given prism round your answer to the nearest whole number
It is not possible to provide a solution without information about the shape of the prism. Please provide additional information.
To find the lateral area of a prism, you need to calculate the sum of the areas of all its lateral faces. The formula for the lateral area (LA) is:
LA = (perimeter of base) * height
Now, let's calculate the lateral area for the given prism:
Base 1: 8.9 m
Base 2: 8 m
Height: 4 m
First, calculate the perimeter of the base:
Perimeter = (Base 1 + Base 2) * 2
= (8.9 + 8) * 2
= 17.9 * 2
= 35.8 m
Now, multiply the perimeter by the height:
LA = Perimeter * height
= 35.8 * 4
= 143.2 m^2
Rounding to the nearest whole number, the lateral area is approximately 143 m^2.
To find the surface area of a prism, you need to calculate the sum of the areas of all its faces. The formula for the surface area (SA) is:
SA = 2 * (area of base) + (perimeter of base) * height
Now, let's calculate the surface area for the given prism:
Base 1: 8.9 m
Base 2: 8 m
Height: 4 m
Calculate the area of one base:
Area of Base = Base 1 * Base 2
= 8.9 * 8
= 71.2 m^2
Calculate the perimeter of the base (as done previously):
Perimeter = (Base 1 + Base 2) * 2
= (8.9 + 8) * 2
= 17.9 * 2
= 35.8 m
Now, calculate the surface area:
SA = 2 * (Area of Base) + (Perimeter * height)
= 2 * 71.2 + (35.8 * 4)
= 142.4 + 143.2
= 285.6 m^2
Rounding to the nearest whole number, the surface area is approximately 286 m^2.
To find the lateral area and surface area of a prism, we need to know the dimensions and the formulas for calculation.
The lateral area of a prism is the sum of the areas of all the lateral faces, while the surface area includes both the lateral area and the areas of the two base faces.
Let's assume the dimensions of the prism are as follows:
Base length = 8.9m
Base width = 47m
Height/Depth = 8m
First, let's calculate the lateral area:
The lateral area formula for a rectangular prism is:
Lateral Area = Perimeter of Base × Height
The perimeter of the base can be calculated as:
Perimeter of Base = 2 × (Base length + Base width)
Using the given values, we have:
Perimeter of Base = 2 × (8.9 + 47) = 2 × 55.9 = 111.8m (rounded to the nearest whole number)
Lateral Area = 111.8m × 8m = 894.4m² (rounded to the nearest whole number)
Next, let's calculate the surface area:
The surface area formula for a rectangular prism is:
Surface Area = 2 × Base Area + Lateral Area
The base area can be calculated as:
Base Area = Base length × Base width
Using the given values, we have:
Base Area = 8.9m × 47m = 418.3m² (rounded to the nearest whole number)
Surface Area = 2 × 418.3m² + 894.4m² = 1730m² (rounded to the nearest whole number)
Therefore, the lateral area of the prism is approximately 894m², and the surface area is approximately 1730m².