Home » Math Theory » Geometry » Perimeter

Perimeter

What is a perimeter?

Perimeter is a closed path that covers or surrounds any two-dimensional shape. We can say that a perimeter is the total distance of any closed shape. Here are the examples of shapes that we can determine its perimeter.

How to find the perimeter?

Finding the perimeter of any two-dimensional shape depends on the number of sides our shape has. Say, for example, we have a triangle and a square. The number of sides a triangle has is 3; hence, we will get the total distance around its three sides.

Now, how do we find the perimeter? Well, we need to start identifying the shape of our figure first, then use a formula in getting the perimeter. Each shape has a different formula in determining the perimeter – and that’s what we will tackle in the next sections.

Circle

The perimeter of a circle is called as the circumference. A circle is still considered a two-dimensional shape even though it does not have a length and width. However, they have radius and diameter. We can determine the circumference of any circle through its radius or diameter.

Finding the Perimeter of a Circle through Radius

The radius is the distance from the center of the circle to any point on the circumference. The image shows the radius of a circle.

Now, to get the circumference of a circle using its radius, we will use the formula

C= 2πr

where C = circumference,

= 3.14 or $\frac{22}{7}$

Example #1

What is the circumference of a circle if the radius is 18 cm?

Solution

Example #2

Find the total distance around the circle with a radius that measures 30 meters.

Solution

Finding the Perimeter of a Circle through its Diameter

The diameter is the longest line segment in any circle. The measure of a diameter is twice the measure of a radius. Hence, the formula of finding the circumference of a circle through its diameter is given by:

C= πd

where C = circumference,

= 3.14 or $\frac{22}{7}$

d = diameter

Example #1

What is the circumference of a circle with a diameter of 13 mm?

Solution

Example #2

Determine the total distance around the circle when the diameter is 46 decimeters.

Solution

Triangle

A triangle is a two-dimensional closed shape with three straight sides. Every triangle has three sides, three vertices, and three angles. If given a triangle, we simply add all the measures of its sides.

The formula in finding the perimeter of a triangle is given by

P = a + b + c

where a, b, and c are the measures of the sides of a triangle.

Example #1

If the measures of the sides of a triangle are 17 cm, 23 cm, and 25 cm, what is its perimeter?

Solution

Example #2

Can you determine the perimeter of a triangle if all three sides measure 19 meters?

Solution

A quadrilateral is any polygon with exactly four sides. There are different kinds of quadrilaterals such as square, rhombus, rectangle, trapezoid, and rhombus.

Square

A square is a quadrilateral where each of its sides is equal. Hence, we can get the perimeter of a square by adding the measures of all four sides or by simply multiplying the measure of one side by 4.

Thus, the formula of finding the perimeter of the square is:

P = 4s

where s is the measure of the side of a square.

Example #1

What is the perimeter of a square where each side measures 10 centimeters?

Solution

Example #2

Determine the total distance around a square where one side measures 27 meters.

Solution

Rhombus

Like squares, a rhombus is a quadrilateral where four sides are equal, and the pair of opposite sides are parallel to each other. Hence, the formula in finding the perimeter of a rhombus is the same as finding the perimeter of a square.

Thus, it is given by the formula

P = 4s

where s is the measure of the side of a rhombus.

Example #1

What is the perimeter of a rhombus if the measure of one side is 9 units?

Solution

Example #2

Find the total distance of a rhombus with a side measure of 35 kilometers.

Solution

Rectangle

A rectangle is a two-dimensional quadrilateral where opposite sides are parallel and equal. The sides of a rectangle are called as a width and length. Thus, the formula given in getting the perimeter of a rectangle is:

P = 2(l + w)

where l = length

w = width

Example #1

What is the perimeter of a rectangle if the length measures 19 centimeters and the width measures 21 centimeters?

Solution

Example #2

Determine the perimeter of a rectangle if the length measures 350 centimeters and the width measures 3 meters.

Solution

Regular Polygon

Regular polygons are two-dimensional geometric figures with a fixed number of sides and where all sides are equal.

Hence, the formula of finding the perimeter of any regular polygon is given by:

P = n(s)

where n = number of sides of a regular polygon

s = measure of the side of a regular polygon

Example #1

What is the perimeter of a 9-sided polygon with side measures of 23 meters?

Solution

Example #2

Determine the perimeter of a five-sided regular polygon where each side measures 11 centimeters.

Solution

What is the formula for finding the perimeter of some closed-shape?

The table below shows the formula for finding the perimeter of some closed-shape.

How to solve problems involving perimeter?

To solve problems that involve finding the perimeter of any closed shape, you may follow the following steps:

1. Identify the shape being described.
2. Make sure that the unit of measurement is always the same.
3. Use the formula for finding the perimeter of the given shape.
4. Always remember to write the proper unit of measurement.

Problem #1

A rectangular field garden measures 45 yards by 60 yards. What is the total distance that surrounds the garden?

Solution

Problem #2

The diameter of a clock measures 10 inches. What is the circumference of the clock?

Solution

Problem #3

A seven-sided regular polygon with a side measure of 13 decimeters is needed for Gwyneth’s project. What is the total distance that surrounds the polygon?

Solution

What is the importance of finding the perimeter?

The use of perimeter is used in our daily lives, especially architects and engineers. Most people who understand the concept of the perimeter can help them design their room, remodel their kitchen, or even build a table or chair. Farmers, gardeners, or even lot owners also use their knowledge in perimeter to fence their lots. More so, perimeters are important in estimating and calculating materials needed for completing a certain projects.