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Section 10.2

- Perimeter and Area

Exam III

- 8.3 - 3D shapes
- 9.1 - Congruence Transformations
- 9.2 - Symmetries and Tesselation
- 9.3 - Similarity (and Congruence)
- 10.2 - Perimeter (of anything) and Area (of

triangles and quadrilaterals only)

Perimeter and Area

- Perimeter is the distance along the border of a

two dimensional shape - Area of a shape is the measure of the

(two-dimensional) space the shape takes up.

Units

- The units for perimeter are units of distance

(e.g. cm, m, ft, mi, yd, ) - The units for area are the square of units of

distance (cm2, m2, ft2, mi2, yd2, ). Here m2 is

read as square meters or meters squared.

Perimeter of polygons

- Find the perimeter for the shape below

13in

6in

Perimeter of polygons

- Find the perimeter for the shape below

7m

Perimeter of polygons

- Estimate the perimeter of the shape below

4cm

Draw this shape, and answer

How would you find the perimeter?

What about this shape?

Find the perimeter in terms of h and b

h

b

Find the perimeter

- Assume the inner and outer rectangles are similar

8

12

9

Tools for measuring perimeter

- Ruler - increases numerical accuracy over

eyeballing it. - Straight edge - increases relative accuracy with

respect to partial information. - String - increases accuracy for the measurement

of curves.

Quadrilaterals

- The classification of quadrilaterals can be used

to help us in making our task of measuring the

perimeter easier.

How much information do we need to find the

perimeter for

Demystifying ?

- Before handing your students the formula for

circumference, have them make connections first.

Formulas can be dangerous

- Equating the task of finding the perimeter to

plugging numbers into a formula is a common

practice that completely obscures the purpose of

a formula. - Especially when that formula seems mysterious,

like C 2?r to be explored later

Shifting from perimeter to area

- Seconds, yards, degrees Celsius, quarts, and

other standard units of measurement have everyday

tools to measure them (stopwatch, yardstick,

thermometer, measuring cup, etc.), but

combination of units almost never have everyday

tools to measure them (m2, foot-pounds, etc.)

Shifting from perimeter to area (2)

- What are some (not necessarily mathematical)

relationships between perimeter and area?

Shifting from perimeter to area (2)

- What are some (not necessarily mathematical)

relationships between perimeter and area? - Formulas often use related numbers (radius,

length, width, etc.) - Both can be considered the defining

characteristic of a shape. (e.g. space enclosed

by a fence, sq. footage of a house, etc.)

Measuring area

- When area is first introduced, why are the shapes

almost always drawn on graph paper? Perimeter

rarely is introduced by drawing shapes on graph

paper, why area?

Consider the shapes A and B below

- Jorge says A has a larger area
- Kate says B has a larger area
- Louis says their areas are equal
- Who is right?

B

A

Geoboards and Area

- Assumption a 1 by 1 square on the geoboard has

an area of 1 unit2

Geoboard Find the area

Geoboard and Area

Geoboard and Area

Geoboard and Area

The process of measuring area

- How could you describe the process for

determining the area of a triangle?

b

Dissection

- How could you describe the process for

determining the area of a triangle?

h

b

Dissection

- How could you describe the process for

determining the area of a triangle?

Do I need to know where the height line

seg Meets the base?

h

b

Surround it

- How could you describe the process for

determining the area of a triangle?

h

b

The process of measuring area

- How could you describe the process for

determining the area of a parallelogram?

h

b

The process of measuring area

- How could you describe the process for

determining the area of a trapezoid?

The process of measuring area

- How could you describe the process for

determining the area of a general polygon?

Formulae

- Area for a rectangle is
- Area for a square is
- Area for a triangle is
- Area for a parallelogram is
- Area for a trapezoid is

Relate the formula with the process

- Explain how the process of finding the area of a

trapezoid can be used to explain the formula for

the area

Area of a circle

- Area of a circle is A pr2
- Why?
- Draw a circle using a compass, and cut it out as

carefully as possible.

Surface Area

- Surface area of a 3 dimensional shape is

analogous to the perimeter of a 2 dimensional

shape - It is the area of the boundary of the three

dimensional object.

Formula for a Cylinder

pr2

2pr

pr2

r

Formula for a triangular prism

b

c

h

H

a

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