10. Perimeterand Area......................................................................................................................
Trianglesand Parallelograms
LearningObjectives
- Understandbasicconceptsof the meaningof area.
- Use formulasto find the area of specifictypesof polygons.
Introduction
Measurementis not a new topic.You havebeenmeasuringthingsnearlyall your life. Sometimesyou use
standardunits (pound,centimeter),sometimesnonstandardunits (yourpace or arm span).Spaceis measured
accordingto its dimension.
- One-dimensionalspace:measurethe lengthof a segmenton a line.
- Two-dimensionalspace:measurethe area that a figuretakesup on a plane(flat surface).
- Three-dimensionalspace:measurethe volumethat a solid objecttakesup in “space.”
In this lesson,we will focuson basicideasaboutarea in two-dimensionalspace.Oncethesebasicideas
are establishedwe’ll look at the area formulasfor someof the mostfamiliartwo-dimensionalfigures.
BasicIdeasof Area
Measuringarea is just like measuringanything;beforewe can do it, we needto agreeon standardunits.
Peopleneedto say, “Theseare the basicunitsof area.”This is a matterof history. Let’s re-createsomeof
the thinkingthat wentinto decisionsaboutstandardunitsof area.
Example 1
Whatis the area of the rectanglebelow?Whatshouldwe use for a basicunit of area?As one possibility, supposewe decidedto use the spaceinsidethis circleas the unit of area.