Measurement of 2D Figures

1
Measurement of 2D Figures

• Math Alliance
• April 5, 2011

2
Process of Measurement

• Decide on the attribute to be measured
• Select a unit that has that attribute
• Fill, cover or match the unit to the attribute of
  the object

3
Investigation

• If the unit of area is a regular sheet of typing
  paper, about what is the area of one side of a
  typical door?
• Individually, develop a conjecture.
• As a table, discuss your conjectures.

4
Big Ideas for Measuring Area

• Area is defined by covering.
• (The Moving Principle) The area of a shape does
  not depend on its position or orientation.  
• (The Combining Principle) Area is additive.

5
Area of Parallelograms Triangles
Area of a Triangle Length x width /2
Area of a Parallelogram Length x width
6
Area of Polygons

• The Johnsons own a lot that has a creek running
  behind it. How could they find the area of the
  lot?

7
How about this?
a
s
8
Or this?
s
a
9
Or This?
10
From Polygons to Circles
Area ½ (a)(p)
Area ?
How do we get from here
to here?
11
Everyday Circles

• Take measurements of your circles
• Which measurements did you use?
• What relationships did you see?

12
Everyday Circles

• How we can we use these measurements to find the
  area of a circle?

13
Homework

• Read Sections 12.1 12.2
• Section 12.1 71, 72, 80, 81, 90, 91
• Turn in 71, 80,
• Section 12.2 2-6, 11, 14, 15, 18, 20, 23, 35,
  36, 37, 44, 57, 58, 67, 69
• Turn in 2-6, 23, 36, 57, 58, 67
• Triangle Problem You are given 1200 m of
  fencing. You need to create a triangular garden.
  What is the largest garden you can make with
  this fencing?