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

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

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

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: 260 + 100 = 360 u²

Example: A regular triangular pyramid has a slant height of 20 cm, a base edge of 24 cm. P = 72 u B = 1443 12 3 24 Lateral Area: ½ 72 × 20 = 720 cm² Total Surface Area: 720 + 1443 ≈ 969.4

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

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.

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.

Example: To find the radius: 51² – 45² = 576 576 = 24 Lateral Area: πrl Π(24)(51) = 1224Π ≈ 3845.3 u² Total Surface Area: πrl + πr² 1224Π + Π 24² = 1800Π u² ≈ 5654.9 u²

Example: Lateral Area: πrl Π(15)(25) = 375Π ≈ 1178.1 u² Total Surface Area: πrl + πr² 375Π + Π(15²) = 600Π u² ≈ 1885.0 u²

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 ≈ 754.0 in² Total Surface Area: πrl + πr² 240Π + Π(12²) = 384Π in² ≈ 1206.4 in²