1. Surface Area, Lateral Area, and Volume of Prisms and Pyramids

2. Lateral Area of a Right Prism (P = perimeter of the base, h = height)
L = Ph
(P = perimeter of the base, h = height)
Perimeter = 2(5) + 2(4) = Perimeter of triangular base
H = = = 19
L = 18 x 8 = H = 4
L = 19 x 4 = 76 6 8 5 4 5 4 8

3. Surface Area of a Right Prism Surface Area = Lateral Area + 2 x area of the base Surface Area = Ph + 2B 6 8 5 4
Lateral area = 18 x 8 = 144
Area of base = 5 x 4 = 20
Total surface area = (20) = 184
Lateral area = 19 x 4 = 76
Area of base = ½ (6)(4) = 12
Total surface area = (12) = 100 5 4 8

4. Volume of a Right Prism V = area of base x height V = Bh6 8 5 4
Area of base =5 x 4 = 20
H = 8
V = 20 x 8 = 160
Area of base = ½(6)(4) = 12
H = 4
V = 12 x 4 = 48 5 4 8

5. Regular Pyramids
A regular pyramid has a base which is always a regular polygon.
The lateral faces all intersect at a point called the vertex and form triangles.
The altitude is a segment from the vertex perpendicular to the base.
The slant height is the height of a lateral face.
vertex
altitude
Lateral side
Slant height
Base

6. Lateral Area of a Regular Pyramid
The lateral area of a regular polygon = ½ pl
( p = perimeter of the base, l = slant height)
L = ½ pl 7 8
Perimeter = 4 x 7 = 28
Slant height = 8
Lateral area = ½ (28)(8) = 112

7. Surface Area of a Regular Polygon
Surface area of a regular polygon = lateral area + area of the base.
Surface area = ½ pl + B
Lateral area = ½ (28)(8)= 112
Area of base = 7 x 7 = 49 7 8
Surface area = = 161

8. Volume of a Right Pyramid
The volume of a right pyramid = 1/3 of the area of the base time the height.
V = ⅓ Bh 6 7 8 5
Area of base = 7 x 6 = 42
Height = 5
Volume = ⅓ (42)(5) = 70

9. Formulae for Lateral Area, Surface Area, and Volume
Prisms:
Lateral area: L = Ph (p = perimeter, h = height)
Total Surface area: T = Ph + 2B (B = area of base)
Volume: V = Bh
Pyramids:
Lateral area: L = ½ Pl (p = perimeter, l = slant height)
Total Surface area: T = ½ Pl + B (B = area of base)
Volume: V = ⅓ Bh ( B = area of base, h = height)