Makeit into a parallelogram.This can be doneby makinga copyof the originaltriangleand puttingthe
copytogetherwith the original.
The area of the parallelogramis , so the area of the triangleis orWarning:Noticethat the height (alsooftencalledthealtitude) of the triangleis theperpendiculardistance
betweena vertexand the oppositeside of the triangle.
Areaof a TriangleIf a trianglehas base unitsand altitude units,then the area, , is or squareunits.orLessonSummary
Oncewe understoodthe meaningof measuresof spacein two dimensions—inotherwords,area—wesaw
the advantageof usingsquareunits.With squareunitsestablished,the formulafor the area of a rectangle
is simplya matterof commonsense.Fromthat pointforward,the formulafor the area of eachnew figure
buildson the previousfigure.For a parallelogram,convertit to a rectangle.For a triangle,doubleit to make
a parallelogram.
Pointsto Consider
As we studyotherfigures,we will frequentlyreturnto the basicsof this lesson—thebenefitof squareunits,
and the fundamentalformulafor the area of a rectangle.
It mightbe interestingto note that the wordgeometryis derivedfrom ancientGreekrootsthat meanEarth
(geo-)measure(-metry).In ancienttimesgeometrywas very similarto today’s surveyingof land.You can
see that land surveyingbecameeasilypossibleonceknowledgeof how to find the areaof planefigures
was developed.
LessonExercises
Completethe chart.Baseand heightare givenin units;area is in squareunits.