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
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 and the perimeter of the rectangle is
Perimeter of a Rhombus: Since a rhombus is defined by having four sides of equal length, the perimeter of the below rhombus is just
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:
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 .
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:
A farmer has a square field whose perimeter is twice its area. What is the area of the field?
Let's say that the field has sides of length . Then, we get Simplifying, we get and thus the area of the field is 4.
1. The outer rectangle below is units apart from the smaller rectangle on the top and bottom sides, and 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?
Let's fill in some details:
Now, we can see that the perimeter of the inner rectangle, , must have a height of 6 units and a base of 6 units. Thus, its perimeter will be 24.
2. The perimeter of a regular -sided shape is Find the length of a side.
Recall that a regular polygon has sides of equal length. Thus, suppose it has a side of length . Then, its perimeter will be and so we get which implies
3. The length of a side of a regular hexagon is What is the perimeter?
This is essentially the same as the previous question, albeit in reverse. Recall that a regular hexagon has six sides of equal length. Thus, if its sides are 6 units long, its perimeter will be units long.