AreaMost people have an intuitive i

Area
Most people have an intuitive idea of what we mean by the area of a geometric figure.However, making our intuitive ideas mathematically precise is not quite so easy.Fortunately, the situation for parallelograms, triangles, and trapezoids is much simpler than for some other figures.

The basic unit that we will use for measuring area is 1 square unit—that is, a square with each side one unit long. The unit of length is arbitrary. A square unit can be 1 cm by 1 cm or 1 foot by 1 foot or 1 mile by 1 mile. Figure G.55 shows 1 square unit.

The area of a geometric figure is defined to be the number of square units needed to precisely cover that figure.

If we consider a rectangle whose dimensions are 3 by 4 units (see Figure G.56), we can see that it contains 12 square units.

Be sure that you do not confuse length, which is measured in basic units such as feet or meters, with area, which is measured in square units such as square feet or square meters. Rather than calling the sides of the rectangle the length and the width, we will refer to them as base and height (you will soon see why these names are preferable). The
base and height are usually labeled as b and h, respectively, as in Figure G.57.

On the basis of our analysis of the case of the 3 by 4 rectangle, which clearly has an area of 12 square units, we can generalize and say that the area of a rectangle is the product of its base and height.

Let us now consider a parallelogram ABCD and let b  the length of side AB. See Figure G.58. We draw a perpendicular from D to side AB and also from C to the extension of side AB at F. Such a perpendicular line from a point to a line is often called
an altitude. Since they are of equal length, we label both of these altitudes as h. All of this is shown in Figure G.58.