The area of the missing faces is 284 in², and the missing dimension is 24 in.
The total surface area of a right rectangular prism is the sum of the areas of its faces. In the image you provided, we are given the areas of two faces: 20 in² and 24 in². To find the total surface area, we need to add the areas of the two missing faces.
Total surface area = 20 in² + 24 in² + area of missing face 1 + area of missing face 2
We are also given that the total surface area is 328 in².
328 in² = 20 in² + 24 in² + area of missing face 1 + area of missing face 2
Subtracting the known areas from both sides, we get the following equation.
area of missing face 1 + area of missing face 2 = 328 in² - 20 in² - 24 in² = 284 in²
Therefore, the area of the two missing faces is 284 in².
To find the missing dimension, we need to look at the two missing faces. We can see that they are both rectangles. The length of one rectangle is 2 in, and the length of the other rectangle is 10 in. Since the two rectangles are part of the same prism, their width must be the same.
Missing dimension = width of rectangle 1 = width of rectangle 2
We are also given that the total surface area of the prism is 328 in². To find the width of the rectangles, we can use the following equation.
328 in² = 2(length of rectangle 1)(width) + 2(length of rectangle 2)(width) + 2(area of missing face 1)
Substituting the known values, we get the following equation.
328 in² = 2(2 in)(width) + 2(10 in)(width) + 2(284 in²)
Subtracting the known areas from both sides, we get the following equation.
4(width) = 328 in² - 2(284 in²)
Dividing both sides by 4, we get the following answer.
width = (328 in² - 2(284 in²)) / 4 = 24 in²
Therefore, the missing dimension is 24 in.