1. Lateral Area & Surface Area Of Pyramids & Cones
Geometry 10:3

2. Notes
Using the Word Bank, label the parts of the pyramid and its net.

3. Notes: Formulas
The formula of the lateral surface area of a pyramid is:
½ Pl
P is the perimeter of the base, l is the slant height.
The formula of the TOTAL surface area of a pyramid is:
½ Pl + B

4. Example: Find the height of a square pyramid
with base edges of 10 and height of 12.
Lateral Area:
First find the slant height by using the Pythagorean theorem: 12² + 5² = 169 The slant height is 13. The perimeter is 40.
½ (40)(13) = 260 u²
Total Surface Area:
= 360 u²

5. Example: A regular triangular pyramid has a slant height of 20 cm, a base edge of 24 cm.
P = 72 u B = 144 3 24
Lateral Area:
½ 72 × 20 = 720 cm²
Total Surface Area:
3 ≈ 969.4

6. Notes
Using the Word Bank, label the parts of the cone and its net.

7. Notes: LATERAL AREA
In a cone, the lateral area is the lateral or side surface of the solid.
The formula is under the figure.
l is the slant height.

8. Notes: Total Surface Area
The total surface area of a cone will be the total surface of the lateral area and the base which is in the shape of a circle.
Which is the sum of the lateral area and the area of its base.

9. Example: To find the radius: 51² – 45² = 576 576 = 24
Lateral Area: πrl
Π(24)(51) = 1224Π ≈ u²
Total Surface Area: πrl + πr²
1224Π + Π 24² = 1800Π u²
≈ u²

10. Example: Lateral Area: πrl Π(15)(25) = 375Π ≈ 1178.1 u²
Total Surface Area: πrl + πr²
375Π + Π(15²) = 600Π u²
≈ u²

11. Example: The radius of a cone is 12 in. and the height is 16 in.
First find the slant height: 12² + 16² = 400
400 = 20 The slant height is 20.
Lateral Area: πrl
Π(12)(20) = 240Π ≈ in²
Total Surface Area: πrl + πr²
240Π + Π(12²) = 384Π in²
≈ in²