1. Use formulas to find the lateral area and surface area of the given prism. Round your nearest answer to the nearest whole number. use the large 19x6 m rectangles on the top and bottom as the bases.
Left corner is 2m, bottom length is 19m, and right face is 6m.
A) 100m^2 ; 328 m^2
B) 304m^2 ; 214 m^2
C) 100m^2 ; 214 m^2
D) 304m^2 ; 328 m^2
If you google this there should be an image as well. I just don't understand how to solve this, is there a certain formula? Thank you so much!
go to hell steve
To find the lateral area and surface area of the given prism, we can use the following formulas:
1. Lateral Area = Perimeter of Base × Height
2. Surface Area = 2 × (Lateral Area) + Area of base
First, let's calculate the perimeter of the base.
The left corner is 2m, the bottom length is 19m, and the right face is 6m.
The total perimeter of the base is given by: Perimeter = 2 × (Left Corner + Bottom Length + Right Face)
Perimeter = 2 × (2 + 19 + 6)
Perimeter = 2 × (27)
Perimeter = 54m
Now, let's calculate the lateral area using the formula:
Lateral Area = Perimeter of Base × Height
Lateral Area = 54m × 6m
Lateral Area = 324m²
Next, let's calculate the surface area using the formula:
Surface Area = 2 × (Lateral Area) + Area of base
Surface Area = 2 × 324m² + (19m × 6m)
Surface Area = 648m² + 114m²
Surface Area = 762m²
Rounded to the nearest whole number:
Lateral Area = 324m²
Surface Area = 762m²
Therefore, the correct answer is option B) 304m² for the lateral area and 214m² for the surface area.
To find the lateral area and surface area of the given prism, you need to understand the formulas involved.
1. Lateral Area: The lateral area refers to the sum of the areas of the lateral faces (the sides) of a solid. It does not include the bases. The formula to find the lateral area of a prism is:
Lateral Area = Perimeter of the base x Height
2. Surface Area: The surface area of a prism refers to the sum of the areas of all its faces, including the bases. The formula to find the surface area of a prism is:
Surface Area = 2(Area of the base) + Lateral Area
Given the dimensions of the prism, let's calculate the required areas:
Base dimensions:
- Length of the base = 19 m
- Height of the base = 6 m
Lateral face dimensions:
- Left corner = 2 m (considered a side length)
- Bottom length = 19 m
- Right face = 6 m
1. Lateral Area:
Since the large 19x6 m rectangles on the top and bottom serve as the bases, we need to find the perimeter of one base. The perimeter of a rectangle is calculated by adding the lengths of all sides. In this case:
Perimeter of the base = 2(Length + Width)
= 2(19 m + 6 m)
= 2(25 m)
= 50 m
Now, we can calculate the lateral area using the formula:
Lateral Area = Perimeter of the base x Height
= 50 m x 2 m
= 100 m²
2. Surface Area:
We already have the lateral area as 100 m². Now, we need to find the area of one base, and multiply it by 2 since there are two bases.
Area of the base = Length x Width
= 19 m x 6 m
= 114 m²
Surface Area = 2(Area of the base) + Lateral Area
= 2(114 m²) + 100 m²
= 228 m² + 100 m²
= 328 m²
Therefore, the correct answers are:
A) 100m² ; 328 m²
sounds like the prism is 19x6 by 2
so, there are two bases and two pairs of rectangular lateral faces. It's just a box, and you only have to add up the two areas of the rectangles.