The Concept of Perimeter

The perimeter of an object refers to the total length of the lines forming the outside of the shape. In order to calculate the perimeter of an object, add up the length of each side of the object.

Circle

The perimeter or circumference, C, of a circle is found using the equation C = 2pr, where r is the radius.

Perimeter = Circumference = 2pr where r is the radius [CE or CI or CD]

Perimeter = Circumference = pd where d is the diameter [DI]

If a circle P has a diameter of 5cm, what is the perimeter of circle P?

Perimeter = pd = 5p

Consider another example:

If a circle D has a circumference of 16p, what is the radius of circle D?

Perimeter = 16p = 2pr

8p = pr

8 = r

Triangle

The perimeter of a triangle is the sum of its three sides. It should be noted that the sum of any two sides of a triangle must be larger than the length of the third side.

What is the perimeter of the following triangle?

Since the triangle is right, one can solve for the length of the unknown side.

x² + 52 = 132

x² = 132 - 52

x² = 169 - 25 = 144

x = 12

Quadrilateral

The perimeter, P, of a quadrilateral is the sum of the four sides. There are shortcuts to finding the perimeter for some quadrilaterals. For squares, P = 4*e where e is the length of a side. For rectangles, P = 2w + 2l. For parallelograms, P = 2x + 2y where x and y are the lengths of the parallel sides.

Square

Perimeter of Square = 4 × e where e is the length of a side.

Consider the following example:

If the figure at right is a square and e is 5cm, what is the perimeter of the square below?

Perimeter_Square = 4(side) = 4(5cm) = 20cm

Parallelogram

Perimeter_{Parallelogram} = 2x + 2y where x and y are the lengths of the parallel sides

Consider the following example:

If the length of side gh is 10cm and the length of side kg is 6cm, what is the perimeter of the parallelogram below?

Perimeter_{Parallelogram} = 2(10) + 2(6) = 32cm

Note: In a parallelogram, opposite sides have the same length.