Fix the mistake: Solid Figures ② (Surface Area)
Surface Area ① Surface Area of a Prism
Surface area is the total area of all the faces of a solid. The surface area of a prism can be found from its net.
Surface area of a prism = 2 × area of the base + lateral surface area
Lateral surface area = (perimeter of the base)×(height)
📘 Example ①
Find the surface area of a rectangular prism with a square base whose side length is 4 cm and a height of 6 cm.
Answer: Area of base = 4×4 = 16 cm². Lateral surface area = 4×4×6 = 96 cm².
Surface area = 16×2 + 96 = 128 cm²
Find the surface area of a rectangular prism with a square base whose side length is 4 cm and a height of 6 cm.
Answer: Area of base = 4×4 = 16 cm². Lateral surface area = 4×4×6 = 96 cm².
Surface area = 16×2 + 96 = 128 cm²
💡 Key Points
- Surface area = 2 × area of base + lateral surface area
- Lateral surface area = perimeter of base × height
Practice Problem
- Find the surface area of a triangular prism with an equilateral triangle of side length 3 cm as its base and a height of 5 cm. (Area of an equilateral triangle = (√3/4)×3² ≒ 3.9 cm² (you may leave √3 as it is))
Answer and Explanation
- Answer: (9√3/4)×2 + 3×3×5 = 9√3/2 + 45 cm². Area of base=(√3/4)×9=9√3/4. Lateral surface area=(3×3)×5=45.
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