1. Surface Area of Pyramids
NOTES 12.2
Surface Area of Pyramids

2. Pyramids: Has only one base (polygon).
Edges are not parallel but meet at a single point called the vertex.
Lateral faces are triangles named by its base.

3. Regular Pyramids: The base is a regular polygon.
Sides are congruent isosceles triangles.

4. Parts of a Pyramid:
altitude of pyramid
Slant height (altitude of lateral surface)
Vertex to the center of the base is the altitude of the pyramid.

5. Find the lateral area & total area of the pyramid.
Find the area of the 4 congruent isosceles triangles.
Find slant height. 8
A = ½bh = ½(12)(8) = 48
LA = 4(48) = 192 units2
Equals area of the base plus lateral area.
Base is a square.
Area = 12(12) = 144
TA = = 336 units2

6. Find the surface area of the given pyramid.
Base
45 ft
50 ft
Area of base = 45(50)
Area of base = 2250
The base is 45ft by 50ft and the overall height is 40ft.
45 ft
50 ft
Find the area of the triangular sides.

7. Find the slant height of the triangle with base of 45.
1, = 2,225
Slant height = 5√89
A = ½bh
A = ½(45)(5√89)
A = √89
2 triangles = 2(112.5 √89) = 225 √89
= 2,122.6 units2
= slant height 2
1, = 2,106.25
Slant height = √
A = ½bh
A = ½(50)(√ )
A = 25√
2 triangles = 2(25√ ) =
50 √ = 2,294.7 units2
Total Area = 2, , ,294.7 = 6,667.3 units2

8. Given a square pyramid
If b = 10, a = 3, h = 10, & x = 2,
find the surface area shaded.
Find the area of the base:
A = 10(10) = 100
Find the slant height:
= slant height2
Slant height = 13
Find area of 4 triangles:
A = 4(½)10(13)
A = 260
Total Area = = 360
Find the area of the triangles at the top pyramid:
Slant height:
= slant height2
Slant height = 2.5
Find area of 4 triangles:
A = 4(½)(3)(2.5) = 15
Surface Area of shaded part = = 345 units2