Surface Area of Pyramids and Cones Vocabulary Regular

* Surface Area of Pyramids and Cones

Vocabulary Regular pyramid- a pyramid whose base is a regular polygon, and the faces are congruent isosceles triangles. Slant height of a pyramid- the distance from the vertex to the midpoint of an edge of the base. Slant height of a cone- the distance from the vertex to a point on the edge of the base.

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.

Additional Example 1 A: Finding the Surface Area of a Pyramid Find the surface area of the pyramid. S=B+ 1 Pl 2 1 S = lw + Pl 2 S = (9 • 9) + S = 81 + 180 Use the formula. B = lw 1 (36)(10) 2 Substitute. = 4(9) = 36 Add. S = 261 m 2 The surface area is 261 square meters. P

Additional Example 1 B: Finding the Surface Area of a Pyramid Find the surface area of the pyramid. S=B+ S= 1 Pl 2 Use the formula. 1 1 bh + Pl B= ½bh. 2 2 1 S = 1 (12)(10. 38) + (36)(6) 2 2 S = 62. 28 + 108 S = 170. 28 The surface area is 170. 28 m 2.

Check It Out: Example 1 A Find the surface area of each pyramid.

Check It Out: Example 1 B Find the surface area of the pyramid

The diagram shows a cone and its net. The blue dashed line is the slant height of the cone, the distance from the vertex to a point on the edge of the base.

Additional Example 2: Finding the Surface Area of a Cone Find the surface area of the cone. Use 3. 14 for . S = r 2 + rl Use the formula. S ≈ (3. 14)(32) + (3. 14)(3)(10) Substitute. S ≈ 28. 26 + 94. 2 Multiply. S ≈ 122. 46 Add. The surface area is about 122. 46 square centimeters.