- Understand the basic concepts of the meaning of area.
- Use formulas to find the area of parallelograms, including rectangles.
The area of a shape is the space inside the perimeter.
You can think of the perimeter as a line you may draw with a pen of the outer border of a shape. The area is what you would paint with a paintbrush in order to fill in the entire shape, painting inside the perimeter line.
In a fenced field, the fence would be the perimeter and the grass in the field would be the area.
In a basketball court, the sidelines would be the perimeter and the wooden court surface would be the area.
In a pool, the ________________ would be the perimeter and the ____________ would be the area.
Area of a Rectangle
If a rectangle has base units and height units, then the area, , is square units.
Area of a Parallelogram
How could we find the area of this parallelogram?
Make it into a rectangle by moving the triangular part:
The rectangle is made of the same parts as the parallelogram, so their areas are the same. The area of the rectangle is , so the area of the parallelogram is also .
Warning: Notice that the height of the parallelogram is the perpendicular distance between two parallel sides of the parallelogram, not a side of the parallelogram (unless the parallelogram is also a rectangle, of course).
If a parallelogram has base units and height units, then the area, , is square units.