3. Examples:
h = 8 h = 4
4
8
B = 5 x 4 = 20 8
B = ½ (6)(4) = 12
4
4 5
5 6
perimeter of base = 2(5) + 2(4) = 18 perimeter of base = 6 + 5 + 8 = 19
L. A.= 18 x 8 = 144 L. A. = 19 x 4 = 76
S.A. = 144 + 2(20) = 184 S. A. = 76 + 2(12) = 100
V = 20 x 8 = 160 V = 12 x 4 = 48
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5. Regular Pyramid
( p = perimeter of the base, l = slant height,
B = base area)
The lateral area of a regular pyramid (L.A.)= ½ lp
Surface area of a regular pyramid (S.A.) = ½ lp + B
The volume of a right pyramid (V)= ⅓ Bh
Example: Perimeter = (2 x 7) + (2 x 6) = 26
Slant height l = 8 ; Height h = 5
8
Lateral area = ½ (8)(26) = 104
5
Area of base = 7 x 6 = 42
Surface area = 104 + 42 = 146
6
Volume = ⅓ (42)(5) = 70
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5
6. Prism and Pyramids Formulas
• Prisms:
• Lateral Area: L.A. = ph (p = perimeter, h = height)
• Surface Area: S.A. = ph + 2B (B = area of base)
• Volume: V = Bh
• Pyramids:
• Lateral Area: L.A. = ½ lp (p = perimeter, l = slant height)
• Surface Area: S.A. = ½ lp + B (B = area of base)
• Volume: V = ⅓ Bh ( B = area of base, h = height)
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