A parallelogram is a quadrilateral (it has four sides). The opposite sides of a parallelogram are parallel. The opposite sides of a parallelogram have the same length, and the opposite angles of a parallelogram have the same measure in degrees.

There are several strategies for finding the area of a parallelogram.

• We can decompose and rearrange a parallelogram to form a rectangle. Here are three ways:

  

  Three identical parallelograms on separate grids, each has a base of four units and a height of three units. First parallelogram, vertical dashed segment extending from the bottom left vertex to the opposite side, forming a triangle. An arrow extends from the triangle to the opposite side of the parallelogram to create a rectangle 4 units wide and 3 units high. Second parallelogram, vertical dashed segment extending from the top right vertex to the opposite side, forming a triangle. An arrow extends from the triangle to the opposite side of the parallelogram to create a rectangle 4 units wide and 3 units high. Third parallelogram, vertical dashed segment through the middle of the parallelogram. An arrow extends from the resulting shape to the opposite side of the parallelogram to create a rectangle 4 units wide and 3 units high.

• We can enclose the parallelogram and then subtract the area of the two triangles in the corner.

  

  Two drawings of parallelograms on grids. On the left, a triangle in the bottom left and top right corner is in white and the center is colored blue. On the right, the image from the left is repeated, but the triangles in the corners are colored yellow. Arrows are drawn from the triangles to the right. The triangles two triangles are joined on the right to form a rectangle.

Both of these ways will work for any parallelogram. However, for some parallelograms the process of decomposing and rearranging requires a lot more steps than if we enclose the parallelogram with a rectangle and subtract the combined area of the two triangles in the corners.

A shaded parallelogram on a grid. Base of three units. Slanted sides that decline 6 vertical units over 9 horizontal units. Parallelogram decomposed by dashed segments into six equal right triangles. Each triangle has a vertical side of 2 units and horizontal side of 3 units. Arrows extend to the left from each of the lower 5 triangles. The resulting shape is a rectangle that is 6 units tall by 3 units wide.