Subjects geometry

Prism Surface Area 81C1E1

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1. **State the problem:** We need to find the surface area of a rectangular prism using its net. 2. **Given dimensions and areas:** - Front and back rectangles area = 12 cm² each. - Dimensions given: length = 8 cm, width = 3 cm, height = 2 cm. 3. **Find the area of the side rectangles:** - Side rectangles correspond to the faces with dimensions height and width. - Area of one side rectangle = height × width = $2 \times 3 = 6$ cm². - Since there are two side rectangles, total side area = $2 \times 6 = 12$ cm². 4. **Find the area of the top and bottom rectangles:** - Top and bottom rectangles correspond to length and width. - Area of one top/bottom rectangle = length × width = $8 \times 3 = 24$ cm². - Since there are two such rectangles, total top and bottom area = $2 \times 24 = 48$ cm². 5. **Calculate total surface area:** - Surface area = sum of areas of all faces. - Front and back total area = $2 \times 12 = 24$ cm². - Side rectangles total area = 12 cm² (from step 3). - Top and bottom total area = 48 cm² (from step 4). 6. **Add all areas:** $$\text{Surface Area} = 24 + 12 + 48 = 84 \text{ cm}^2$$ **Final answers:** - Side rectangles area = 12 cm² - Top and bottom rectangles area = 48 cm² - Surface area = 84 cm²