Area refers to the space inside a two-dimensional object, like a square or an octagon, while volume refers to the space that a three-dimensional object takes up, or the internal capacity of that object. Units of area include square feet or square meters, while units of volume include cubic feet or cubic meters.
Calculating the area of an object involves a formula that includes the multiplication of its dimensions. For example, calculating the area of a square requires multiplying the length of a side by itself. Calculating the area of a triangle requires multiplying the triangle's base by the height and dividing that number in half. The basis of the calculation for both shapes (one dimension times the other) is the same, but different shapes require slight alterations to the basic formula.
Calculating the volume of an object also involves a formula to multiply the dimensions, but in the case of volume, there are three dimensions to consider. Calculating the volume of a cube works similarly to calculating the area of a square, except the cube has a third dimension, so the process involves multiplying that side by itself three times. Finding the volume of a triangular prism also involves adding a third dimension to the formula for the area of a triangle.