Area and Volume

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What You Need:

  • Ruler or tape measure
  • Pencil
  • Paper
  • Calculator (optional)

Simply stated, area and volume is all about space. Area is the amount of space taken up by 2-dimensional closed figures, while volume is the amount of space occupied by 3-dimensional objects. Below are the area and volume formulas for the basic shapes in geometry. They may look intimidating to your child, but with a little practice, these formulas will be a piece of cake.

Area Formulas




length x width


base x height


base x height / 2


height x (base1 + base2) / 2


pi*x radius2 **


Volume Formulas



Rectangular Prism

side1 x side2 x side3


(4/3) x pi x radius3


pi x radius2 x height


(1/3) x pi x radius2 x height *


(1/3) x (base area) x height


**radius=the distance from the center of the circle to the outside edge

What You Do:

  1. Have your child make a list of objects around the house that he can use for finding area and volume. Encourage him to try to find at least one example of each shape. For example, a sheet of paper is an example of a rectangle, a stop sign is an octagon, a refrigerator is a rectangular prism, a soda can is a cylinder, a soccer ball is a sphere, etc.
  2. Give him a ruler or tape measure to measure the objects’ dimensions, rounding each measurement to the nearest inch.
  3. Then have him use the formulas above to find the area and volume of each object. He can use paper and pencil to calculate his answers, or you may allow the use of a calculator, depending upon your child's familiarity with these types of equations.

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