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The figure below is a net for a right rectangular prism. Its surface

area is 328 in² and the area of some of the faces are filled in below.
Find the area of the missing faces, and the missing dimension.

The figure below is a net for a right rectangular prism. Its surface area is 328 in-example-1
User Liang Wu
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1 Answer

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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.

User Winestone
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