9.2+Area

Section 9.2 - Area
Area is measured in square units, such as square inches or square meters.



Rectangles

The formula for the area of a rectangle (or square) is length times width. The answer will include square units.

Circles

The area of a circle = (pi)(radius)(radius) or pi times radius squared.

Triangles

Area of a triangle = (1/2)(base)(height)

Parallelograms

Area of a parallelogram = (base)(height) Notice: the height is not the same as the width.

Trapezoids Area of a trapezoid = (top + bottom) / 2 times (height)


 * Combined Shapes**

Complex shapes made of multiple shapes offer an extra fun challenge for calculating area. The shape at the right, for example, can be thought of as multiple rectangles. Calculate the areas of rectangles and you will be able to either add or subtract to get the area of the combined shape.

The image below shows three ways to picture and calculate the area of the combined shape.



Combined shapes may also involve both rectangles and circles. This may require adding or subtracting the area of shapes or parts of shapes.




 * Surface Area**

If you were measuring a parking lot, the area of the lot and the surface area would be the same thing. However, the concept of surface area is different when you start looking at three dimensional objects. Take a square block, for example. The surface area would be the area of each of the six sides. You could find the area of a single side and multiply by six, but only for a square block. If the shape were rectangular, you would have to measure the area for more than one side, though not more than three sides would be different.

One shape that is a bit different is called a cylinder. A cylinder is like a pop can -- something that is round, but flat on both ends. The surface area would be the area of the top, the bottom, and the outside of the circular part. Picture a label on a soup can. The label wraps around the can in a circular shape, but if you cut it off of the can, it is actually a rectangle. The height of the can is the width of one side of the label, but the other side of the label is actually the circumference of the top or bottom of the can.

To calculate the surface area of a cylinder you would need to know if the top and bottom were to be included, or just the "label part."


 * Chapter Nine Practice Problems**

**Where to from here?**
9.1 Perimeter and Circumference 9.2 Area 9.3 Volume Chapter Nine Summary Chapter Nine Homework