Subjects geometry

Triangular Prism Surface 8Aae6E

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1. **State the problem:** Find the surface area of a triangular prism given its net. 2. **Identify the shapes in the net:** The net consists of one rectangle and two triangles. 3. **Given dimensions:** - Rectangle: length = 8 in, width = 5 in - Triangles: base = 3 in, height = 4 in 4. **Formula for surface area of a prism:** $$\text{Surface Area} = \text{Area of rectangular face} + 2 \times \text{Area of triangular face}$$ 5. **Calculate the area of the rectangle:** $$\text{Area}_{rectangle} = 8 \times 5 = 40$$ 6. **Calculate the area of one triangle:** $$\text{Area}_{triangle} = \frac{1}{2} \times 3 \times 4 = 6$$ 7. **Calculate total area of two triangles:** $$2 \times 6 = 12$$ 8. **Calculate total surface area:** $$40 + 12 = 52$$ **Final answer:** The surface area of the triangular prism is **52 square inches**.
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