Question

1. decompose and rearrange this parallelogram to form a rectangle. what is the area of the parallelogram? show your thinking.

Explanation:

Step1: Identify base and height

Count the number of grid - squares for the base and height of the parallelogram. The base of the parallelogram is 6 units and the height is 4 units.

Step2: Use the area formula

The area formula for a parallelogram is \(A = b\times h\), where \(b\) is the base and \(h\) is the height. Substitute \(b = 6\) and \(h = 4\) into the formula.
\(A=6\times4 = 24\) square units.
To form a rectangle from the parallelogram, we can cut off a right - triangle from one side of the parallelogram and move it to the other side. For example, if we cut off the right - triangle on the left side of the parallelogram (formed by the slanted side and the vertical grid - lines) and move it to the right side, we will get a rectangle with the same base and height as the original parallelogram. Since the area of a rectangle is also \(A = b\times h\), and the area of the parallelogram is equal to the area of the rectangle formed from it, the area of the parallelogram is 24 square units.

Answer:

The area of the parallelogram is 24 square units.