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Area formula

All of the area formulas for general convex quadrilaterals apply to parallelograms. Further formulas are specific to parallelograms:

A parallelogram with base b and height h can be divided into a trapezoid and a right triangle, and rearranged into a rectangle, as shown in the figure to the left. This means that the area of a parallelogram is the same as that of a rectangle with the same base and height:

The base × height area formula can also be derived using the figure to the right. The area K of the parallelogram to the right (the blue area) is the total area of the rectangle less the area of the two orange triangles. The area of the rectangle is

and the area of a single triangle is

Therefore, the area of the parallelogram is

Another area formula, for two sides B and C and angle θ, is

Provided that the parallelogram is not a rhombus, the area can be expressed using sides B and C and angle γ {\displaystyle \gamma } at the intersection of the diagonals:

When the parallelogram is specified from the lengths B and C of two adjacent sides together with the length D of either diagonal, then the area can be found from Heron's formula. Specifically it is

where S = (B + C + D 1) / 2 {\displaystyle S=(B+C+D_{1})/2} and the leading factor 2 comes from the fact that the chosen diagonal divides the parallelogram into two congruent triangles.