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Parallelograms: Area and Perimeter

Aparallelogramis aquadrilateralin which both pairs of opposite sides areparallel.

It can be shown that opposite sides of parallelogram must becongruent, that opposite angles are alsocongruent, and that consecutive angles aresupplementary.

Thearea $A$of a parallelogram is given by the formula

$A=bh$,

where$b$is the length of one base and$h$is the height. (The figure below shows how to find the height of a parallelogram.)

Theperimeterof a parallelogram is the sum of the lengths of its four sides.

For example, in the figure below, if$PQRS$is a parallelogram, then we know opposite sides are congruent, so$PQ=10$and$PS=6$.

Therefore, the perimeter is$6+10+6+10$or$32$cm.