use formulas to find the lateral and surface area of the given prism "A rectangular prism is shown. The height is 2 meters, the width is 7 meters, and the length is 12 meters."
Lateral Area = Perimeter of base x Height
Perimeter of base = 2(length + width) = 2(12 + 7) = 2(19) = 38 meters
Lateral Area = 38 meters x 2 meters = 76 square meters
Surface Area = 2lw + 2lh + 2wh
= 2(12)(7) + 2(2)(12) + 2(2)(7)
= 168 + 48 + 28
= 244 square meters
To find the lateral area and surface area of a rectangular prism, we can use the following formulas:
1. Lateral Area: The lateral area of a prism is the sum of the areas of all its lateral faces. For a rectangular prism, the lateral area can be calculated using the formula: Lateral Area = 2lh + 2wh, where l is the length, w is the width, and h is the height.
2. Surface Area: The surface area of a prism is the sum of the areas of all its faces, including the base(s) and the lateral faces. For a rectangular prism, the surface area can be calculated using the formula: Surface Area = 2lw + 2lh + 2wh.
Given:
Height (h) = 2 meters
Width (w) = 7 meters
Length (l) = 12 meters
Using these values, we can now calculate the lateral area and surface area of the given prism.
1. Lateral Area:
Substituting the values into the formula, we have:
Lateral Area = 2lh + 2wh
Lateral Area = 2(12)(2) + 2(7)(2)
Lateral Area = 48 + 28
Lateral Area = 76 square meters
2. Surface Area:
Substituting the values into the formula, we have:
Surface Area = 2lw + 2lh + 2wh
Surface Area = 2(12)(7) + 2(12)(2) + 2(7)(2)
Surface Area = 168 + 48 + 28
Surface Area = 244 square meters
Therefore, the lateral area of the given rectangular prism is 76 square meters, and the surface area is 244 square meters.