Surface Areas of Surface Areas of PyramidsPyramids

Section 11.7

Find the Surface Area…

Find the surface area of a cylinder with a diameter of 10cm and a height of 15cm.

Pyramid

Pyramid – A three dimensional figure in which one face, the base, is any polygon and the lateral faces are triangles that meet at a common vertex.

vertex

The altitude of a pyramid is the perpendicular segment from the vertex to the plane of the base.

The length of the altitude is called the height.

Height

h

Pyramid

Regular Pyramid – a pyramid whose base is a regular polygon.

Slant Height – the length of the altitude of the lateral face.

Slant Height

Pyramid

Lateral Area and Surface Area of a Regular Pyramid

PL2

1

Lateral Area

Base Perimeter

Slant Height

BLS Surface

AreaLateral Area

Base Area

B

Find the surface area of a square pyramid with base edges 5 m and slant height 3 m.

m 3

m 5

SURFACE AREA OF CONESSection 11.3b

A cone has a circular base and a vertex that is not in the same plane as a base.

In a right cone, the height meets the base at its center.

The height of a cone is the perpendicular distance between the vertex and the base.

The slant height of a cone is the distance between the vertex and a point on the base edge.

Height

Lateral Surface

The vertex is directly above the center of the circle.

Baser

Slant Height

r

r

Find the surface area of the cone to the nearest tenth.

4 in.

6 in.