# Volume and Area

Area is a geometric measure that represents the volume that represents the magnitude of a 3-D shape or figure on the flat, two-dimensional plane. Surface area is the equivalent on the three-dimensional surface of an object. This is why it is used when modeling a room and why it is also used for measuring different objects, whether they are objects in three dimensions or in two dimensions.

Geometric shapes represent the simplest form of three-dimensional geometric models. A cube, for example, is a simple geometric shape because it is composed of three faces – one vertical, one horizontal – and one center point. The three faces make a cube, but the center point and the horizontal and vertical axes, which are parallel to the faces, provide a common basis for its surface. The edges and angles in this cube are not only parallel to the axis, they are perpendicular to the faces and to each other.

Flat surfaces are the basic geometric shapes and models. These surfaces are very simple because all their edges are straight to each other and to the faces. Geometric surfaces can be found in nature, as well as man-made materials. They include, for example, the surface of any solid object, the surfaces of many flat surfaces, the surfaces of almost all triangles, squares, hexagons and other polygonal shapes, the surfaces of nearly all of the solids formed by the interlocking of two or more cylinders, and the surfaces of all triangles and squares formed by the interlocking of two or more pentagons. These objects are just the basic geometric surfaces of solid objects.

When we speak of the surface of an object, what we mean is a flat, level surface, and that is what we mean by area in a three dimensional perspective. But what are the other three dimensions of the three dimensional world?

Volume is the amount of space that represents the area of the shape on a flat surface. This volume is the sum of the area and the length of the shape on the flat surface. This volume is also the volume of space that represents the size of the shape on a two dimensional surface.

Length is the length of the shape. It is a constant quantity, so that the volume of the length of the shape is equal to the volume of the area and the length of the space, which is proportional to the length.

Width is the width of the shape. It is a constant quantity, so that the volume of the width of the space is equal to the volume of the area and the length of the space, which is proportional to the length.

Height is the height of the shape. It is a constant quantity, so that the height of the space and the height of the length are proportional to the length. It is usually measured in meters.

Area and volume, like length and width, are both the sum of the length multiplied together. This gives us the sum of all three quantities, area, length, and height.

We have seen that the sum of the length multiplied together give us the height of a three dimensional object. And the height of an object is given by its length. So the height of the object is the volume of the shape in the area of the object. This makes it easy to determine height with a three dimensional perspective.

In fact, this is true of all three dimensional objects, and not just the two dimensional shapes that are covered by this statement. It is true of any three dimensional shapes. The height of a circle, for instance, gives the volume of the circle and the radius of the circle, and the area of the circle, given the volume, gives the length of the circle, and the radius of the circle. And it is true of any three dimensional shapes, whether or not it is a sphere.

There is another way to know the volume of a three dimensional object, but it is not as simple as it seems. The volume is the sum of the length and the height of the shape. 