Calculating Parallelogram Area: Formulas And Applications

Area of a parallelogram

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The area of a parallelogram can be found by multiplying the base by the height. The base is one of the parallel sides of the parallelogram and the height is the perpendicular distance between the base and the opposite side. Using this formula, we can write:

Area = base x height

Alternatively, we can use the formula:

Area = magnitude of the cross product of two adjacent sides

If we have two vectors that represent adjacent sides of a parallelogram, we can find the magnitude of their cross product to determine the area of the parallelogram.

For example, suppose we have a parallelogram with sides represented by vectors u = <2, 3> and v = <4, -1>. To find the area of the parallelogram, we can take the cross product of u and v as follows:

u x v = (2)(-1) – (3)(4) = -2 – 12 = -14

The magnitude of this cross product is |u x v| = |-14| = 14. Therefore, the area of the parallelogram is 14 square units.

It’s important to note that the base and height of a parallelogram must be perpendicular to each other, and the height must be measured from the base to the opposite side. If the height is not directly given, it can be found by drawing a perpendicular line from the opposite side to the base.

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