Surface Area of Right Pyramids

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.

Lateral Area of a Pyramid

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.

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

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

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

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

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?

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

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?

HW: Surface Area of Pyramids Worksheet

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 = = 84 ft²

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