The perimeter is just the distance it would take if you were to walk the outside edges of a given shape. So, for the following triangle:

the perimeter is just a + b + c.

Finding the perimeter of a square or a rectangle is similarly straightforward:

Perimeter of a Square or Rectangle: In the following diagrams, the perimeter of the square is x + x + x + x = 4x and the perimeter of the rectangle is h + b + h + b = 2(b+h).

Perimeter of a Rhombus: Since a rhombus is defined by having four sides of equal length, the perimeter of the below rhombus is just x + x + x + x = 4x.

Perimeter of a Trapezoid:

The perimeter of a trapezoid is a little trickier, but recall that we can break a trapezoid up into two right triangles and a rectangle:

And then, if we have the bases of the right triangles, we can use the Pythagorean Theorem to find the length of the diagonal bits:

Thus, we get that the perimeter is: b_1 + \sqrt{b_3^2 + h^2} + \sqrt{b_4^2 + h^2} + b_2.

Perimeter of a Parallelogram
Remember that the parallel sides of a parallelogram have the same length. Thus, for the below parallelogram:

the perimeter is just a + b + a + b = 2(a+b).

 

include some simpler problems here for finding the perimeter of when they give you basically all the right information

Sometimes, the perimeter figures in a word problem. So, for example, you might have:

Example 1

A farmer has a square field whose perimeter is twice its area. What is the area of the field?

Answer

Practice Problems

1. The outer rectangle below is 3 units apart from the smaller rectangle on the top and bottom sides, and 1 units apart on the left and right sides. The outer rectangle has a base of 8 units and a height of 12 units. What is the perimeter of the inner rectangle?

Answer

2. The perimeter of a regular 33-sided shape is 160\pi. Find the length of a side.

Answer

3. The length of a side of a regular hexagon is 6. What is the perimeter?

Answer

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