it as a rectangle.Oncewe do this, we can derivenew formulasfrom the old ones.
We’ll also needto reviewbasicfactsaboutthe trapezoid,rhombus,and kite.
Areaof a Trapezoid
Recallthat a trapezoidis a quadrilateralwith one pair of parallelsides.The lengthsof the parallelsidesare
the bases.The perpendiculardistancebetweenthe parallelsidesis the height,or altitude,of the trapezoid.
To find the area of the trapezoid,turn the probleminto one abouta parallelogram.Why?Becauseyou already
knowhow to computethe area of a parallelogram.
Makea copyof the trapezoid.Rotatethe copy.Put the two trapezoidstogetherto form a parallelogram.Two thingsto notice:
- The parallelogramhas a basethat is equalto +.
- The altitudeof the parallelogramis the sameas the altitudeof the trapezoid.
Now to find the area of the trapezoid:
The area of the parallelogramis base altitude=.
The parallelogramis madeup of two congruenttrapezoids,so the area of eachtrapezoidis one-half
the area of the parallelogram.The area of the trapezoidis one-halfof.