Section 8.1

The area of a plane figure is the measure of the region enclosed by the figure. You measure the area of a figure by counting the number of square units that you can arrange to fill the figure completely.

You probably already know many area formulas. Think of the investigations in this chapter as physical demonstrations of the formulas that will help you understand and remember them.

How can you find the area of these three rectangles?

Any side of a rectangle can be called the base. A rectangle’s height is the length of the side that is perpendicular to the base. For each pair of parallel bases, there is a corresponding height.

The area formula for rectangles can help you find the areas of

many other shapes.

Find the area of this shape.

Think of the shape this way

The area is 32+3+5+9+3 or 52 square units.

You can also use the area formula for a rectangle to find the area formula for a parallelogram.

Just as with a rectangle, any side of the parallelogram can be called the base. BUT THE HEIGHT OF THE PARALLELOGRAM IS NOT NECESSARILY THE LENGTH OF A SIDE.

base

base

An altitude is any segment from one side of the parallelogram perpendicular to a line through the opposite side. The length of the altitude is the height.

The altitude can be inside or outside the parallelogram. No matter where you draw the altitude to the base, its height should be the same, because the opposite sides are parallel.

Area of a Parallelogram

Find the height of a parallelogram that has area 7.13 square meters and base length 2.3 meters.