- Carpetfor floors,paintfor walls,fertilizerfor a lawn,and more:areasneeded.
Tech Note- GeometrySoftware
You saw earlierthat the area of a rhombusor kite dependson the lengthsof the diagonals.This meansthat all rhombiand kites with the samediagonallengthshavethe samearea.Try usinggeometrysoftwareto experimentas follows.- Constructtwo perpendicularsegments.
- Adjustthe segmentsso that one or both of the segmentsare bisected.
- Drawa quadrilateralthat the segmentsare the diagonalsof. In otherwords,drawa quadrilateralfor
whichthe endpointsof the segmentsare the vertices. - Repeatwith the sameperpendicular, bisectedsegments,but makinga differentrhombusor kite. Repeat
for severaldifferentrhombiand kites. - Regardlessof the specificshapeof the rhombusor kite, the areasare all the same.
The sameactivitycan be doneon a geoboard.Placetwo perpendicularrubberbandsso that one or both
are bisected.Thenplaceanotherrubberbandto form a quadrilateralwith its verticesat the endpointsof the
two segments.A numberof differentrhombiand kitescan be madewith the samefixeddiagonals,and
thereforethe samearea.
LessonExercises
Quadrilateral has vertices and in a coordinateplane.
- Showthat is a trapezoid.
- Whatis the area of?
- Provethat the area of a trapezoidis equalto the area of a rectanglewith heightthe sameas the height
of the trapezoidand baseequalto the lengthof the medianof the trapezoid. - Showthat the trapezoidformulacan be usedto find the area of a parallelogram.
- Sashadrewthis plan for a woodinlay he is making.