1. Surface Area of Right Pyramids

2. Slant Height of a Pyramid The height of a lateral face of a pyramid is called the slant height. The symbol for slant height is a cursive l.

3. Lateral Area of a Pyramid

5. You can form a parallelogram by splitting the triangles into two halves and putting them back together. The lateral area of the pyramid and the area of the parallelogram are equal.

6. Lateral Area of a Pyramid So the lateral area of the pyramid equals the base of the parallelogram times the height of the parallelogram. LA = base of parallelogram · height of parallelogram The base of the parallelogram is 1/2 the perimeter of the base of the pyramid and the height of the parallelogram is the same as the slant height of the pyramid. LA = 1/2 perimeter of base · slant height So the lateral area of a pyramid equals 1/2 the perimeter of its base p times its slant height l. LA = 1/2 pl

7. Surface Area of a Pyramid The surface area of a pyramid equals the lateral area plus the area of the base. Surface Area = Lateral Area + area of base SA = LA + B

8. Part 1 Example 1 What is the surface area of the square pyramid?

9. Part 1 Example 2 What is the surface area of the square pyramid?

10. Part 2 Example 1 Ms. Adventure brought home an assortment of tea from India. To the nearest square inch, how much cardboard was used to make the regular triangular pyramid package?

11. Part 2 Example 2 To the nearest square foot, what is the surface area of the regular triangular pyramid?

12. Part 3 Example You want to make a tent that has the shape of a regular hexagonal pyramid with the dimensions shown. To the nearest square foot, how much fabric do you need?

13. HW: Surface Area of Pyramids Worksheet

15. Example Find the area of every side, add them together. Area of a hexagon = 6(1/2*b*h) Area of a triangle = 1/2*b*h 6(1/2(3.5*3)) A = 31.5 A = 8.75 **Remember there are 6 of these triangles** So, 8.75 * 6 = 52.5 31.5 + 52.5 = 84 ft²

16. 3 m 4 m 5 m