12.3 Surface Area of a Pyramids and Cones Slant Height ( l )

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Presentation transcript:

12.3 Surface Area of a Pyramids and Cones Slant Height ( l )

Definition of a Regular Pyramids A regular pyramid is a pyramid whose base is a regular polygon and whose vertex forms a segment with the center of the polygon perpendicular to its plane.

Part of a Pyramid h is Height from base to vertex l is Slant height, The height of the triangle

Theorem Surface Area of a Regular Pyramid B is for base Area P is for perimeter l is for Slant height

Surface Area of a Regular Pyramid Let r = 3; h = 4 Find the Perimeter r is half the base edge

Surface Area of a Regular Pyramid Let r = 3; h = 4 Find the Perimeter r is half the base edge Base edge is 2(3) = 6 Square perimeter 4(6) = 24 P = 24

Surface Area of a Regular Pyramid Let r = 3; h = 4 ; P = 24 Find the Base Area

Surface Area of a Regular Pyramid Let r = 3; h = 4 ; P = 24 ; B = 36 Find the Base Area Base edge is 6 Base Area = (6) 2 B = 36

Surface Area of a Regular Pyramid Let r = 3; h = 4 ; P = 24 ; B = 36 Find the Slant Height l Right Triangle

Surface Area of a Regular Pyramid Let r = 3; h = 4 ; P = 24 ; B = 36 ; l = 5 Find the Slant Height l Right Triangle side legs 3 and = l = 25 = l 2 l = 5

Surface Area of a Regular Pyramid Let r = 3; h = 4 ; P = 24 ; B = 36 ; l = 5

Surface Area of a Regular Pyramid Let r = 4; h = ; P = 24 ; B = ; l = 9 Find the Base and Perimeter

Surface Area of a Regular Pyramid Let r = 4; h = ; P = 24 ; B = ; l = 9 Find the Base and Perimeter

Surface Area of a Regular Pyramid Let r = 4; h = ; P = 24 ; B = ; l = 9 Find the Surface Area

Surface Area of a Regular Pyramid Let r = 4; h = ; P = 24 ; B = ; l = 9 Find the Surface Area

Surface of a Cone Finding the Base is Easier, since it is a circle.

Surface of a Cone Finding the Surface Area. r = 5, h = 12

Surface of a Cone Finding the Surface Area. r = 5, h = 12; need l

Surface of a Cone Finding the Surface Area. r = 5, h = 12; need l

Surface of a Cone Finding the Surface Area. r = 5, h = 12; need l

Homework Page #15 – 43 odd

Homework Page # even,