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Lateral Area &Surface Area Of Prisms
Geometry 10:2
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Warm-up 1. Find the area of a rectangle with sides:
a. 6 and 9 b. 11 and 4 c. 52 and 86 2. If the area of a square is 36 units², what are the lengths of the sides? 3. If the area of a square is 45 units², what are the lengths of the sides?
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Notes
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Right Prism This is a pentagonal prism.
Right Prism: A prism where all the lateral faces are perpendicular to the bases.
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Oblique Prism: This also is a pentagonal prism.
Oblique Prism: A prism that leans to one side and the height is outside the prism.
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Right Prisms vs Oblique Prisms
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Right Prisms vs Oblique Prisms
Right Prism – Edges are Altitudes.
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Formulas The formula of the lateral surface area of a prism is
Lateral area = P×h P is the perimeter of the base The formula of the TOTAL surface area of a prism is Surface Area = P×h + 2B B is the area of the base.
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Example: Lateral Area: 16 + 12 = 28 28 × 2 = 56 cm² Surface Area:
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Example: Lateral Area: 32 × 4 = 128 Surface Area: 10² – 6² = 64
b² = 64 b = 8 (8 × (12/2) × 2) = 224 un²
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Example: Lateral Area: 6² + 8² = 100 b² = 100 b = 10 24 ×12 =288 yd²
Surface Area: (6×8÷2)(2) + 288 = 336 yd²
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Example: Lateral Area: (6+5+12+5) × 10 28 × 10 = 280 un² Surface Area:
((6+12)÷2)×4 = 36 = B 2(36) = 352 un²
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Example: Lateral Area: 8 × 6 × 11 = 528 in² Surface Area:
(360÷6÷2) = 30 4 ÷ tan(30) = 6.9 Area of this hexagon is × 2 = 332.6 = 860.6
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