What is the difference between area and perimeter?

The perimeter is the distance around the shape. The area is the amout of space inside the shape's outline.

Accompanying Resources:  Area of a Rectangle Boom Cards (digital task cards), Area & Perimeter Boom Cards , Perimeter Boom Cards ​If you've ever switched the two of these up before, you're not the only one!  The goal of this lesson is to help you understand the difference between area and perimeter.  In simplest terms: area is the amount of space inside a shape, and perimeter is the distance around the outside of the shape. Let's look at some examples together. Area measures the number of square units that can fit on the inside of a shape. If you copied a shape onto grid paper, the area would be the number of squares that the shape covers up.  There are many different formulas for area that depend on the shape, but the main idea is that area is the amount of space on the inside of the shape. 10 squares fit inside the shape below, so the area is 10 square units.​ ​Area is the number of squares that fit in the inside of the shape so it is always measured in square units​ (square meters, square inches, square feet, etc.).​ Perimeter measures the distance around the outside of the shape.  Think about it as if you're about to put a fence around the outside of the shape and you need to know the length of the fence.  If you count the spaces around the outside of the shape below, you'll find that the distance around it is 14. This means the perimeter is 14 units.

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Perimeter measures length, or distance. It is always measured in regular units​ (feet, inches, meters, etc.).​

Can you answer these area and perimeter questions on your own? Click the START button below to try a practice quiz.

How is volume different from perimeter and area ?

The perimeter of a shape represents the distance around it, the area of a shape is the surface or flat space that the shape covers (in 2D) while the volume of a shape is the space it occupies in real life (in 3D).  

To understand the difference between perimeter, area and volume, let’s define each of them in detail :

Definition of perimeter

The perimeter of a shape is the total length of its figure, also known as the sum of the length of all its sides. Perimeter is measured by adding up the length of its numerous sides. For example, if we are looking to calculate the perimeter of a rectangle, we must start by adding up the length of its four sides. Since the parallel sides of a rectangle are always equal, you only need to find the length of two sides.

Definition of area

The area of a shape is the amount of space that is inside its sides or edges (i.e., the size of the flat, closed surface that the shape covers). The area is measured in square units and is usually calculated by multiplying the shape’s length by its width. However, depending on different polygons, it can have different formulas.

For example, if we are looking to calculate the area of a square, we need to multiply its length by its width. Since the sides of a square are all equal, we need to multiply the size of one side by itself.

Definition of volume

The volume of a shape is the amount of 3D space that the shape occupies.  The volume is measured in cubic units due to the fact that it is calculated by multiplying the shape’s area by its height. Since the height is always evaluated in regular units (meters, centimeters…) and the area in square units (square meters, square centimeters…), volume is given in cubic units (cubic meters, cubic centimeters…).

For example, if we are looking to calculate the volume of a cylinder, we have to multiply the area of the base (in this case it’s the area of one of the circles) by the height of the cylinder. The height of a cylinder is the distance between its two circles and the area is either given or must be calculated.  

How do you find the perimeter of a geometric shape ?

To calculate the perimeter of a geometric shape, you have to add up the length of all its sides. If we have a rectangle with the length a and the width b, the formula for the perimeter P is :

P= a+a+b+b

And since the rectangle has two parallel sides, the formula becomes

P= 2a+2b

P= 2(a+b)

Example 1 

The length and width of a rectangle are 8 cm and 3 cm, respectively.

The perimeter of this rectangle is P = 8+8+3+3 = 2 x (8+3) = 22 cm

Now, suppose we have a square. The formula for the perimeter P of this square is :

P = a+a+a+a

P = 4a

Example 2 

The sides of a square are 7 cm.

The perimeter of this square is P = 7+7+7+7 = 4 x 7 = 28 cm

How do you find the area of a geometric shape ?

To calculate the area of a geometric shape, you have to multiply its length by its width. Let’s take the same figures to avoid any confusion :

If we have a rectangle with the length a and the width b, the formula for the area A of this rectangle is :

A = a x b

Example 1 

The height of the rectangle is 12 cm and the width is 5 cm.

The area of the rectangle is A = 12 x 5 = 60 cm2

P.S : Don’t forget to add the square unit ( 2 ) when calculating the area.  

Now, suppose we want to calculate the area of a square, the formula for the area A is :

A = a x a

A = a2

Example 2 

The sides of the square we want to study are 9 cm each.

Therefore, the area of the square is A = 9 x 9  = 92 = 81 cm2

How do you find the volume of a geometric shape ?

Moving on to the volume. To calculate the volume of a geometric shape you have to multiply the shape’s area by its height.

To illustrate this, we are going to stick with the same figures and calculate the volume of a right rectangular prism and a cube. We are also going to calculate the volume of a cylinder to clarify the formula even more :

– For a right rectangular solid where the area A is given and the height is h, the formula to calculate the volume V is :

V = A x h

Example 1 

The area and height of a right rectangular prism are 38 cm2 and 6 cm, respectfully.

The volume of this rectangular solid is V = 38 x 6 = 228 cm3

P.S : Don’t forget to add the cubic unit ( 3 ) when calculating the volume.  

For a cube, it’s a little bit special. If the area is A and the height h, the formula for the volume of the cube V is :

V = A x h

But, since it’s a cube, the sides are equal to its height so the area is b2. The formula for the volume V of the cube can therefore be expressed as follows :

V = b2 x b

V = b3

Example 2 

The cube has sides of 12 cm each.

The volume of this cube is V = 123 = 1728 cm3

For a cylinder, let’s suppose the area A of the circle was given as well as its height h. The formula of the volume V of the cylinder is :

V = A x h

If the area was not given, we must calculate it first. So the formula becomes :

V = A x h

V = π x r² x h

… with r being the radius of the circle. 

Example 3

Our cylinder has a height of 9 cm and a circle radius of 4 cm.

To find the volume of this cylinder, we must find the area first, which in this example is:

A = π x r² = 3.14 x 4² = 50.24 cm2

Now, we can calculate the volume of the cylinder:

V = A x h = 50.24 x 9 = 452.16 cm3

P.S : Keep in mind that the numbers stated in all of these examples were in the same units, so if they weren’t, it would be important to convert them.  

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