The figure below is a net for a right rectangular prism. Its surface area is 246 ft² and the area of some of the faces are filled in below. Find the area of the missing faces, and the missing dimension.

Question

72 ft²
72 ft²
27 ft²
27 ft²
9 ft
9 ft
8 ft
8 ft
8 ft
8 ft
?
?
A
A

The area of each missing face is
ft²
The length of each missing edge is
ft

Answer 1

To find the area of the missing faces, we need to subtract the area of the given faces from the total surface area.

Total surface area = 246 ft²
Given area = 2(72 ft²) + 2(27 ft²) + 2(8 ft x 9 ft) = 144 ft² + 54 ft² + 144 ft² = 342 ft²
Missing area = 246 ft² - 342 ft² = -96 ft²

This means that there is an error in the given values, as we cannot have negative area. We can try to find the missing dimension to see if there is a mistake.

Let the dimensions of the prism be length (L), width (W), and height (H).
From the net, we can see that:
- L = 2(8 ft) + 9 ft = 25 ft
- WH = 27 ft², so either W or H is 9 ft and the other is 3 ft.
- LW = 72 ft², so either L or W is 8 ft and the other is 9 ft.

We can check these possibilities using the equation for total surface area:

Total surface area = 2(LW + LH + WH)
If L = 25 ft, W = 9 ft, and H = 3 ft, then:
Total surface area = 2(25 ft x 9 ft + 25 ft x 3 ft + 9 ft x 3 ft) = 246 ft²
This matches the given value, so this is the correct solution.

The missing dimension is the width, which is 8 ft. Therefore, the missing faces have areas of 9 ft² and 25 ft².

Missing area = 9 ft² + 25 ft² = 34 ft²
Missing edge length = 8 ft

Final answer:
The area of each missing face is 9 ft² and 25 ft².
The length of each missing edge is 8 ft.