Answer:
The lateral area of the prism is 190 square inches and the total surface area is 358 square inches.
Explanation:
To find the lateral area and total surface area of a rectangular prism, we need to use the following formulas:
Lateral Area = perimeter of the base x height
Total Surface Area = 2 x base area + lateral area
Where the base area is simply the product of the length and width of the rectangular prism.
Let's apply these formulas to the rectangular prism with dimensions 12in x 7in x 5in:
Lateral Area:
To find the perimeter of the base, we add up the lengths of all four sides of the rectangle:
Perimeter of the base = 2(length + width) = 2(12in + 7in) = 2(19in) = 38in
Now, we multiply the perimeter of the base by the height of the prism:
Lateral Area = 38in x 5in = 190in^2
Therefore, the lateral area of the rectangular prism is 190 square inches.
Total Surface Area:
To find the base area, we simply multiply the length and width of the rectangular prism:
Base Area = length x width = 12in x 7in = 84in^2
Now, we can use the formula for total surface area:
Total Surface Area = 2 x base area + lateral area
Total Surface Area = 2(84in^2) + 190in^2
Total Surface Area = 168in^2 + 190in^2
Total Surface Area = 358in^2
Therefore, the total surface area of the rectangular prism is 358 square inches.
So the lateral area of the prism is 190 square inches and the total surface area is 358 square inches.