What is Perimeter In Math? - Definition & Area
Perimeter definition
Perimeter is the sum of the measure of every side of a 2D shape, or the sum of the measure of every side of a 3D shape measuring on the ground or floor.
When you take the perimeter of a shape, you measure around it. This is a good thing, since the word "perimeter" comes from two Greek words meaning, "to measure around."
Round shapes (ovals, circles, ellipses and such) have perimeter, but we almost always call that measure circumference. For any circle, the relationship between circumference, C, (the circle's perimeter) and its diameter, d, is a fixed ratio:
Perimeter is always a linear measure. Use the same units given for each side, like mm, foot, and so on.
Perimeter of a triangle
The simplest polygon is the triangle, with three straight sides enclosing an area. To find the perimeter, P, of any triangle, you need to know the length each of the three sides, s:
Most triangles are not designated with s1, s2, and s3; most illustrations use the letters a, b, and c opposite the angles A, B, and C:
A couple of shortcuts are available for perimeter of triangles. Isosceles triangles have two congruent sides called legs, so you can simply double one of them and add the third side:
P = s1 + s2 + s3
P = 21 m + 21 m + 19 m
P = 2(21 m) + 19 m
P = 42 m + 19 m
P = 61 m
Equilateral triangles have three congruent interior angles and therefore three congruent sides. So if you know one side, you know all three and the perimeter.
Draw or imagine an equilateral triangle with one side labeled as 43mm. What is it's perimeter?
P = s1 + s2 + s3
P = 43 mm + 43 mm + 43 mm
P = 3(43 mm)
P = 129 mm
Perimeter of a square or rhombus
A square or rhombus has four congruent sides. Knowing the measure of one side, s, gives you the measure of all sides. The formula is:
What is the perimeter of a rhombus (a leaning square) with sides 37 cm?
P = 4s
P = 4(37 cm)
P = 148 cm
For Physical Education, your group presented a class project. You invented an outdoor game that uses a square field with sides of 17 yards. What is its perimeter?
P = 4s
P = 4(17 yards)
P = 68 yards
Perimeter of a rectangle or parallelogram
The perimeter of a rectangle (or parallelogram) is found by doubling the sum of its width, w, and side length (not height), l:
Let's say you have a rectangle for the long sides labeled 5.7 m and the short sides labeled 4.3 m. What is its perimeter?
P = 2(w + l)
P = 2(5.7 m + 4.3 m)
P = 2(20 m)
P = 40 m
Here is a parallelogram with a short side length of 73 inches and width of 113 inches. What is its perimeter?
P = 2(w + l)
P = 2(113" + 73")
P = 2(186")
P = 372"
Unless the problem asks you, do not convert the answer to another unit (like feet and inches).
Perimeter of an n-gon
What do you do when you have a pentagon (five sides), octagon (eight sides), enneadecagon (19 sides), or n-gon (n sides)? You follow the same steps as with easier polygons:
If you have the measurements, you can add to find perimeter. Proceed with caution:
Be careful that every side uses the same measurement unit; and
Be certain you have the measurement of every side; and
Check to see if the shape is a square, rhombus, rectangle or parallelogram (so you do not need every side labeled); and
Be careful to add each side only one time
An easy way to organize yourself is to pick a starting side, right its measurement, then proceed clockwise around the shape.
Try it!
Here are some final perimeter problems to try.
What is the perimeter of a square with one side 89 feet long?
What is the perimeter of an equilateral triangle with one side measuring 197 mm?
And here is a tough one: The perimeter of a rectangle is 144 yards. The rectangle's long side is 49 yards. How long is the rectangle's short side?
Did you get answers of 356 feet, 591 mm, and a short side of 23 yards? We hope so!