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Rule

Area of a Parallelogram

The area of a parallelogram is equal to the product of its base

b

and height

h .

The base can be any side of the parallelogram and the height is the perpendicular distance to the opposite side.

The area of a parallelogram can also be calculated by multiplying the lengths of two non-parallel sides by the sine of the angle between them.

Proof

Using Base and Height

Consider a parallelogram where the base and the height are known. Drawing a diagonal divides the parallelogram into two triangles. Therefore, the area of the parallelogram can be written as the sum of the areas of the triangles.

Notice that the base and height of the parallelogram are also the base and height of each of the triangles. Use the fact that the area of a triangle is half the product of its base and its height to derive an expression for the area of the parallelogram in terms of its base and height.