# How to Find the Perimeter of a Geometric Figure

Perimeter is a measure of the distance around a two-dimensional shape. To calculate the perimeter of a rectangle, for example, add the size of its four sides (the two horizontal and the two vertical). To determine the perimeter value of any other non-circular geometric figure, do the same, adding the sizes of each of the outer sides. Knowing how to measure the perimeter of a certain area is very useful in everyday life. Imagine that someone wants to build a yard fence. In order to buy the exact measure of materials, she will need to calculate the total perimeter of the area. So, to save trips to the building materials warehouse, or to study for the test, learn to calculate the perimeter now!

## Steps

### Part 1 of 2: Finding the Perimeter of Most Geometric Shapes

#### Step 1. Find the size of each side

Although there are formulas to facilitate the calculation of the perimeter of some geometric figures, basically, it is enough to add the sides. The important thing to start with is knowing the size of each side.

• In the case of a pentagon, for example, you will need to know the size value of each of its five sides.
• Even for an irregular twenty-sided polygon it is possible to calculate the perimeter, as long as the size of all sides is known.

#### Step 2. Add the size of all sides together

This is valid for any non-circular object. Follow the exercise:

• What is the perimeter of a pentagon whose sides have the following values: A = 4, B = 2, C = 3, D = 3, and E = 2?
• Answer: 4 + 2 + 3 + 3 + 2 = 14, therefore P (perimeter) = 14.

#### Step 3. Working with variables

Find the perimeter even when the sides are represented by variables. Consider a triangle where the sides have the values: 14a, 11b and 7a:

• Sum all sides: P = 14a + 11b + 7a;
• Combine the common terms: P = (14a + 7a) + 11b;
• P = 21a + 11b.

#### Step 4. Remember the measurement units

In an exercise, it is not always known which measurement unit is used to calculate the perimeter (millimeters, centimeters, meters, etc.). However, in the real world, this is very important to take into account (how do you buy 10 fence?). In the case of the pentagon exercise, for example, if the unit used to represent the values ​​of the sides was centimeters, the result should be written as: P = 14 cm.

### Part 2 of 2: Learning the formulas for calculating perimeter

#### Step 1. Find the perimeter of a circle

Some regular figures have formulas just to make calculation easier, while others, like the circle, require the use of a formula. The perimeter of a circle is called the circumference, and to find it, use the formula: C (circumference) = 2πr.

• The first step is to find the radius of the circle, which is the length from the center to the edge, determined by a straight line segment.
• π is a constant number, equivalent to 3, 14. Despite being an infinite decimal, one can use the presented version (3, 14) to obtain approximate values.
• For a circle of radius 4 cm, the count would be: C = 2 x 3, 14 x 4 = 25, 12 cm.

#### Step 2. Find the perimeter of a triangle

For this, adopt the equation: P = a + b + c. For example, if a triangle has the following measurements: a = 20 cm, b = 11 cm and c = 9 cm, we arrive at P = 20 + 11 + 9 = 40 cm.

#### Step 3. Calculate the perimeter of a square

All sides of a square are equal, so the formula is P = 4x, where x represents the size of each side.

### In a square of side x = 3 cm, the bead will look: P = 4 x 3 = 12 cm

#### Step 4. Find the perimeter of a rectangle

In a rectangle, the parallel sides are the same size, so the formula is: P = 2a + 2b, where “a” equals horizontal sides and “b” equals vertical. For a rectangle with sides a = 8 cm and b = 5 cm:

• P = (2 x 8) + (2 x 5);
• P = 16 + 10;
• P = 26 cm.
• The equation P = 2(a + b) will generate the same answer: 2(8 + 5) = 2(13) = 26 cm.

#### Step 5. Find the overall perimeter of quadrilaterals

A quadrilateral is any geometric figure that has four closed sides. These include rectangles, squares, trapezoids, parallelograms, deltoids and diamonds. See the three equations available:

• For a quadrilateral with all different sides, such as an irregular trapezius: P = a + b + c + d;
• For one with all sides equal: P = 4x (same formula as square);
• For those that have equal parallel sides (like a rectangle): P = 2a + 2b or P = 2(a + b).