11-1 Space Figures and Cross Sections

Polyhedra• A polyhedron is a three-

dimensional figure whose surfaces are polygons.

• Each polygon is a face of the polyhedron.

• An edge is a segment that is formed by the intersection of two faces.

• A vertex is a point where three or more edges intersect.

• A regular polyhedron is one where all the faces are congruent regular polygons.

Identifying Vertices, Edges, and Faces

How many vertices, edges, and faces are in each polyhedron?

Cross Sections

• A cross section is the intersection of a solid and a plane.

What is the cross section formed by the plane and the solid?

11-2 Surface Areas of Prisms and Cylinders

Prisms

• A prism is a polyhedron with two congruent, parallel faces, called bases.

• The other faces are lateral faces.• A prism is named by the shape of its bases.

More About Prisms

• The altitude, or height, of a prism is the perpendicular distance between the bases.

• In a right prism, the lateral faces are rectangles and a lateral edge is an altitude.

• In an oblique prism, some or all of the lateral faces are nonrectangular.– Assume prisms are right prisms unless stated or

pictured otherwise.

Lateral and Surface Areas

• The lateral area (LA) of a prism is the sum of the areas of the lateral faces.– The product of the perimeter of the BASE and the height

of the prismLA = Ph

• The surface area (SA) is the sum of the lateral area and the area of the two bases (ALL surfaces).

SA = LA + 2B

Finding Surface Area of a Prism

• What is the surface area of the prism?

Answer each of the following:

• What is the lateral area of the prism?

• What is the area of the base?

• What is the surface are of the prism?

Cylinders

• A cylinder is a solid that has two congruent parallel bases that are circles.

• The altitude, or height, is the perpendicular distance between the bases.– In a right cylinder, the segment joining the centers of

the bases is the height.– In an oblique cylinder, it is not. – Assume cylinders are right, unless stated or

pictured otherwise.

Cylinder Areas

• If you were to “unroll” a cylinder, the resulting rectangle is the lateral area.

LA = 2πrh• The surface area is the sum of the lateral area and the areas

of both bases.SA = LA + 2πr2

Finding Surface Area of a Cylinder

• The radius of the base of a cylinder is 4 in. and its height is 6 in. What is the surface area of the cylinder in terms of π.

The radius of the base of a cylinder is 10 cm and its height is 9 cm. What is the surface area of the cylinder in terms of π.