  Why are there so many different formulas for area? Many students become dependent on applying formulas, but they forget the formulas soon after the chapter test. You can help students by focusing on the general formula that area is length by width.

Area is a measurement of square units. When a rectangle is drawn on a grid, the square units form equal rows. So, multiply the length of a row by the number of rows. Because the length and width must be perpendicular to each other to create squares, some books call these the base and height measurements. However, it's usually better to think of two-dimensional measurements as length and width. If you draw any line segment across a parallogram, parallel to a base, that segment will always be the same length as the base. And the width is measured perpendicular to the base. So, the area is still the length by width. Think of the "average" distance across a trapezoid as the length of a segment midway between the two parallel bases. One way to find the average is to add the two lengths and divide by 2. To find the area, multiply this average length by the width. Does this work for triangles?
Yes. For triangles the average width is the distance across the middle, which is half of the base. Again, multiply by the width, measured from the base (or an extension of the base) to the opposite vertex. 