We want to think about how to use the area of a rectangle to find the area of a parallelogram. First, remember that the area of a polygon is how much surface it covers. Let's first look at the area of a rectangle that has a length of l and a width of w by drawing it on a grid.
In this example, the length l is 4 units and the length w is 6 units. We can find the area by multiplying the side lengths of the rectangle.
Area of the Rectangle&= 4( 6)
&=24 unit^2
Because the side length of a square in the grid is 1 unit, the area of these squares is 1 unit squared.
Area of Each Square&=1(1)
&=1 unit^2
This means that we can also find the area of the rectangle by counting the squares inside the rectangle. Now we will cut the rectangle that we drew into two pieces that can be rearranged to form a parallelogram. Then we will construct a parallelogram using the pieces. Let's do it.
The area of a parallelogram is equal to the area of a rectangle when one side length of the rectangle equals the base of the parallelogram and the other side length equals the height of the parallelogram.
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Area of Parallelogram & Area of Rectangle
A= b h & A= l w
We can use the area of a rectangle to find the area of a parallelogram because these shapes are so closely related. The formula for the area of a parallelogram comes from the formula for the area of a rectangle.
