PANORAMA 12

From Polygons to Polyhedrons

UNIT 12.1: POLYGONSSI UNITS

Remember: KING HENRY DIED MOTHER DIDN’T CARE MUCH Km hm dam m dm cm mm For basic units X10 per step going from

left to right, ÷10 per step going from right to left

Ex: change into km:10cm,100dam,52mm,17hm Ex: change into mm: 33km, 6dm, 11cm,

86.5dm

SI UNITS OF AREA For area you can still follow:

KING HENRY DIED MOTHER DIDN’T CARE MUCH

However, the only difference is multiply by X100 going from left to right, and ÷100 from right to left.

The reason for this is since the units are squared we assume 10 X 10 = 100

Therefore, every step you will have to multiply or divide by 100

APOTHEM OF A REGULAR POLYGON

The apothem is the measure from the center of the polygon (shape) to the center of one side.Apothe

m

AREA OF A REGULAR POLYGON There are 2 methods for finding the

area of a polygon: POLYGON: has 5 sides or more ex:

pentagon, hexagon, etc.

Method 1: Triangle method1. Divide the polygon into triangles2. Find the area of 1 triangle3. Use: A= AT x NT

(AT= area of triangle, NT= number of triangles)

Use the apothem as your height and the length of your side as your base

Method 2: Perimeter method1. Find the perimeter of your polygon2. Use A= (p= perimeter, a=

apothem)

DECOMPOSABLE POLYGONS AND SUBTRACTING AREAS

Some situations you may have to break up the shape into more manageable pieces (decomposing).

Some situations you may have to subtract areas. It is always the bigger area minus the smaller area.

Remember you cannot have a negative area.

CLASSWORK AND HOMEWORK

Textbook P 175-176 #1-10

Workbook P 56-59

UNIT 12.2: SOLIDS A solid is an amount of space that is

surrounded by a closed surface.

Face: flat or curved surface bounded by edges

Edge: Line of intersection between two faces

Vertex: a corner shared by more than two edges

How many edges, faces, and vertices does each

solid have?

NET OF A POLYHEDRON A polyhedron is like a solid. It only has

flat sides no curved surfaces (sphere, cone, cylinder)

A net of Polyhedron is when you unfold the surface.

In a net every face must share a common edge with another face.

Draw the net of the following;

PRISMS A prism is a polyhedron with to congruent

parallel faces, called bases. Bases are connected by lateral faces

(always rectangles)

Lateral faces Bases

Prisms are identified according to the shape of the base.

A right prism is one whose lateral faces are rectangles

A regular prism is one that is base is a regular polygon

PYRAMID A pyramid is a polyhedron with a base

and whose lateral faces are triangles. All faces meet at a common point

called an apex.

HOMEWORK AND CLASSWORKTextbook P 185-188

Workbook p 60-63

UNIT 12.3: AREAS PRISMS AND PYRAMIDS The height of a prism is the distance

between the two bases. The height of a pyramid is the distance

between the apex and the base. The apothem of a pyramid is the

distance from the apex to the center of one side of the base.

AREA OF THE BASE To find the area of the base of a

pyramid or prism simply use your formulas given in Panorama 10.

Remember that pyramids have 1 base and prisms have 2.

2m5m

LATERAL AREA: PRISM The lateral area is the sum of the areas

of all the faces of a polyhedron, excluding the bases

There are two ways to find lateral area.1. Find the area of 1 face, using formulas

from panorama 10. Then multiply by the number of faces.

3cm

2cm

The second method you must use:A= perimeter of base X height

1.5m8.2m

LATERAL AREA: PYRAMID This is the area of the faces excluding

the base. There are two ways to find it as well.1. Add the area of each of the triangular

faces2. A= perimeter of base X apothem 2A= 5cm

h= 4.5 cmSide= 3cm

TOTAL AREA AND DECOMPOSABLE SOLIDS Total area is the sum of the lateral area

and the area of the base or bases. A= lateral area + area of base or

bases A decomposable solid follows the same

rules as the total area. However, you must subtract the area of

the base or side where the solids are joined.

HOMEWORK AND CLASSWORKTextbook P 195-198

Workbook p 64-67

UNIT 12.4: DETERMINING UNKNOWN MEASUREMENTS To solve unknown measurements,

ex: when the height, apothem, etc. are not given, you must;

1. Make sure that there is only one piece of information that is missing.

2. Follow notes from unit 10.3 “Solving equations” (algebra)

SOLVING EQUATIONS When solving equations your objective is to

get an answer for your letter (missing value).1. Remember your must get all your letters on

one side and numbers on the other.2. Start with addition and subtraction. Bring

them to the other side and change the sign.3. Remember to keep your variable positive. 4. Get rid of multiplication and division, by

doing the opposite operations.

5. Get rid of any numbers that are squared, by taking the square root.REMEMBER YOUR UNITSTextbook p. 202-204 #1-12Workbook p. 68-71