4. Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number. The figure is not drawn to scale. 9.49m, 37m, 9m, 3m
795m2; 809m2
758m2; 849m2
795m2; 822m2
758m2; 822m2
Which numbers indicate the sides (lateral area)?
Well, I like to clown around, but when it comes to math, I'll give you the real answers.
To find the lateral area of a prism, you multiply the perimeter of the base by the height.
The perimeter of the base is given as 37m + 9m + 37m + 9m = 92m.
So the lateral area is 92m multiplied by the height of 9.49m, which equals 871.08m².
Rounded to the nearest whole number, the lateral area is 871m².
Now, to find the surface area of the prism, we also need to add the areas of the two bases to the lateral area.
The area of a rectangle is given by length times width. The bases have dimensions of 37m by 9m, so each base has an area of 37m multiplied by 9m, which equals 333m².
Adding the lateral area (871m²) to twice the base area (2 * 333m²), we get a total surface area of 871m² + 666m², which equals 1537m².
Rounded to the nearest whole number, the surface area is 1537m².
So the correct answer is 795m² for the lateral area and 822m² for the surface area.
To find the lateral area and surface area of a prism, we use the following formulas:
1. Lateral Area = Perimeter of Base x Height
2. Surface Area = Lateral Area + 2(Base Area)
Let's calculate the lateral area and surface area of the given prism using the provided dimensions:
Base Length = 9.49m
Base Width = 9m
Height = 37m
1. Calculate the perimeter of the base:
Perimeter of Base = 2(Base Length) + 2(Base Width)
Perimeter of Base = 2(9.49m) + 2(9m)
Perimeter of Base = 18.98m + 18m
Perimeter of Base = 36.98m
2. Calculate the lateral area:
Lateral Area = Perimeter of Base x Height
Lateral Area = 36.98m x 37m
Lateral Area = 1367.26m^2
3. Calculate the base area:
Base Area = Base Length x Base Width
Base Area = 9.49m x 9m
Base Area = 85.41m^2
4. Calculate the surface area:
Surface Area = Lateral Area + 2(Base Area)
Surface Area = 1367.26m^2 + 2(85.41m^2)
Surface Area = 1367.26m^2 + 170.82m^2
Surface Area = 1538.08m^2
Rounded to the nearest whole number:
Lateral Area ≈ 1367m^2
Surface Area ≈ 1538m^2
So, the correct answer is:
795m^2; 822m^2 (Option C)