1. **State the problem:** We have a net of a right rectangular prism with some face areas and dimensions given. The total surface area is 340 m². We need to find the area of the missing faces and the missing dimension (length of the unknown edge). 2. **Identify known dimensions and areas:** - Two faces have area 50 m² with one dimension 10 m. - Two faces have area 80 m² with one dimension 8 m. - One face has unknown area and unknown dimension (denote missing length as $x$). 3. **Find missing lengths from given areas:** - For the 50 m² faces: area = length × width = 50, one side is 10 m, so the other side is $\frac{50}{10} = 5$ m. - For the 80 m² faces: area = length × width = 80, one side is 8 m, so the other side is $\frac{80}{8} = 10$ m. 4. **Assign dimensions:** - Let the prism dimensions be $x$, 8 m, and 10 m. - From above, the missing length $x$ is the unknown dimension. 5. **Calculate total surface area formula:** $$\text{Surface Area} = 2(lw + lh + wh)$$ where $l = x$, $w = 8$, $h = 10$. 6. **Plug in known values and solve for $x$:** $$340 = 2(x \times 8 + x \times 10 + 8 \times 10)$$ $$340 = 2(8x + 10x + 80)$$ $$340 = 2(18x + 80)$$ $$340 = 36x + 160$$ $$340 - 160 = 36x$$ $$180 = 36x$$ $$x = \frac{180}{36} = 5$$ 7. **Find missing face areas:** - Missing face with dimensions $x$ and 8 m: area = $5 \times 8 = 40$ m². - Missing face with dimensions $x$ and 10 m: area = $5 \times 10 = 50$ m². **Final answers:** - Area of each missing face: 40 m² and 50 m². - Missing edge length: 5 m.