1. **State the problem:** We have a net of a right rectangular prism with some face areas given and some missing. The total surface area is 396 ft². We need to find the area of the missing faces and the missing dimension. 2. **Identify known dimensions and areas:** The prism has dimensions length $l$, width $w$, and height $h$. From the net: - Two faces have area 42 ft² with one side 6 ft, so the other side is $\frac{42}{6} = 7$ ft. - Two faces have area 72 ft² with one side 6 ft, so the other side is $\frac{72}{6} = 12$ ft. - The vertical faces have height 7 ft and unknown width $x$ (the missing dimension). 3. **Assign dimensions:** From the above, - Height $h = 6$ ft (from the vertical side of the horizontal rectangles) - Width $w = 7$ ft (from the vertical rectangles with height 7 ft) - Length $l = 12$ ft (from the horizontal rectangles with area 72 ft²) 4. **Calculate missing face areas:** The missing faces are the two vertical rectangles with dimensions $7$ ft (height) and $x$ ft (width). Since the prism is rectangular, the missing dimension $x$ corresponds to length $l = 12$ ft. Area of each missing face $A = 7 \times 12 = 84$ ft². 5. **Verify total surface area:** Surface area $S = 2(lw + lh + wh)$ Calculate each term: $$lw = 12 \times 7 = 84$$ $$lh = 12 \times 6 = 72$$ $$wh = 7 \times 6 = 42$$ Sum: $$84 + 72 + 42 = 198$$ Total surface area: $$2 \times 198 = 396$$ ft², which matches the given total. **Final answers:** - Area of each missing face: $84$ ft² - Length of each missing edge: $12$ ft