PRISMSand

FRUSTUMBy: Alwin Ng, Ong Von Wan, Phares Phung, Chloe The, Yip Xiao Jung, David Tan, Carol Tang, Alison

WHAT ARE PRISMS?

1.A solid object with identical ends.2.Has flat sides (no curves)3.Has a cross section.

Questions Involving Prisms1. Surface AreaCalculated by multiplying base area by 2 and adding the perimeter of base multiplied by height.

2.Volume of prismBase area multiplied by height

3. Area and volume of cross section (Frustum)

TYPES OF PRISM•There are 6 main types of prism

A prism is a polyhedron, which means all faces are flat!

NET OF A PRISM

Determined by shape of base

Determined by number of sides

Regular and Irregular Prisms

•All the previous examples are Regular Prisms, because the cross section is regular (in other words it is a shape with equal edge lengths, and equal angles.)•

Here is an example of an Irregular Prism:

It is "irregular" because the cross-section is not "regular" in shape.

Regular

PRISMS: RIGHT AND OBLIQUERight Prism: It is a geometric

solid that has a polygon as its base and vertical sides perpendicular to the base.

Oblique Prism: The joining edges and faces are not perpendicular to the base faces.

SURFACE AREA OF A PRISMArea = 2b + ph

b = area of a basep = perimeter of a baseh = height of the prism

Ex:Surface Area = 2(½ X 8 X 3) + [(8+5+5) X 12]= 240 cm2

VOLUME OF A PRISM

Volume = bhb = area of baseh = height

Example:Volume = (½ X 8 X 3) X 12 = 144 cm3

FRUSTUM OF A PRISMWhen a plane section taken is not parallel to the ends, the portion of the prism between the plane section and the base is called frustum.

Perpendicular cut

Non-parallel cut

Cross Section

Frustum

In figure ABCEFGHI represents a frustum of a prism whose cutting plane EFGH is inclined at an angle θ to the horizontal. In this case, the frustum can be taken as a prism with base ABEF and height BC.

Volume of frustum= Area ABEF x BC= (BE+FA)/2 x BA x BC

Surface area of frustum= Area of Base+ Area of Cross Section+ Area of lateral surface

= BC(BA) + Area of Base/ cos θ + Area of trapezium and rectangle