2. Sunshine State Standards
MA.7.G.2.1 Justify and apply formulas for surface area..of…pyramids…and cones.
Also MA.7.G.2.2

3. Vocabulary
regular pyramid
slant height of a pyramid

4. Pyramid – A three dimensional figure in which one face, the base, is any polygon and the lateral faces are triangles that meet at a common vertex.
vertex
Pyramid

5. The length of the altitude is called the height.
The altitude of a pyramid is the perpendicular segment from the vertex to the plane of the base.
The length of the altitude is called the height.
Height
Pyramid

6. The base of a regular pyramid is a regular polygon, and the faces are congruent isosceles triangles.
The diagram shows a square pyramid. The blue dashed line labeled l is the slant height of the pyramid, the distance from the vertex to the midpoint of an edge of the base.

7. Lateral Area and Surface Area of a Regular Pyramid
Base Perimeter
Slant Height B
Surface Area
Lateral Area
Base Area

9. Additional Example 1A: Finding the Surface Area of a Pyramid
Find the surface area of the pyramid. 1 2
S = B Pl
Use the formula.
S = lw + Pl 1 2
B = lw
S = (9 • 9) (36)(10)‏ 1 2
Substitute P = 4(9) = 36
S =
Add.
S = 261 m2
The surface area is 261 square meters.

10. Additional Example 1B: Finding the Surface Area of a Pyramid
Find the surface area of the pyramid. 1 2
S = B Pl
Use the formula.
S = bh Pl 1 2
B= ½bh.
S = (12)(10.38) (36)(6)‏ 1 2
S =
S =
The surface area is m2.

11. Check It Out: Example 1A
Find the surface area of each pyramid.
S = B + Pℓ =(7)(7) (28)(12) 1 2
S = = 217
= 217 mm2

12. Check It Out: Example 1B
Find the surface area of the pyramid 1 2 1 2
S = B Pℓ
B = (8)(6.9) = 27.6
S = (8+8+8)(5.6) = 1 2
S = 94.8
= 94.8 m2