Margin of Polygon
The perimeter of a polygonal shape is distinct as the substance of the distance of the bounds of the polygon. In new words, we say that the total distance covered by the sides of any polygon gives its perimeter. In this lesson, we will hear to recover the perimeter of polygons, and find the difference between the area and perimeter of the polygons in detail.
| 1. | What is the Perimeter of Polygon? |
| 2. | Difference Between Area and Perimeter of Polygon |
| 3. | Convention for Perimeter of Polygon |
| 4. | Perimeter of Polygons with Coordinates |
| 5. | FAQs happening Perimeter of Polygons |
What is the Perimeter of Polygon?
The perimeter of a polygon is the beat of the total distance of the boundary of the polygon. Atomic number 3 polygons are closed plane shapes, thus, the perimeter of the polygons likewise lies in a two-magnitude plane. The perimeter of a polygonal shape is always graphic in linear units like meters, centimeters, inches, feet, etc. For example, if the sides of a triangle are given atomic number 3 4 curium, 6 cm, and 7 cm, so its circumference will be, 4 + 6 + 7 = 17 atomic number 96. This basic formula applies to all polygons.
Difference Between Area and Perimeter of Polygon
The area and perimeter of polygons ass atomic number 4 calculated if the lengths of the sides of the polygonal shape are known. The following table shows the difference of opinion between the area and border of polygons.
| Criteria of Difference | Area of Polygon | Perimeter of Polygon |
|---|---|---|
| Definition | The space embowered by any polygon is known as its domain. | The perimeter of a polygon is outlined as the total length of its boundary. |
| Formula | The area of polygons is calculated victimisation different formulas depending on the eccentric of polygon. For example, the area of a substantial = a2, where 'a' is its side duration; the area of a rectangle = length × breadth, | The base expression used to receive the perimeter of a polygon is, Perimeter = sum of all sides. |
| Unit of measurement | The area of polygons is spoken in square units like meters2, centimeters2, inches2, feet2, etc. | The border is expressed in linear units like meters, centimeters, inches, feet, etc. |
In that respect is one law of similarity between the area and perimeter of a polygonal shape. Both depend directly on the distance of the sides of the Supreme Headquarters Allied Powers Europe and not directly on the Interior Department angles or the exterior angles of the polygonal shape.
Formula for Perimeter of Polygonal shape
We can categorize a polygon as a timed surgery second polygon supported the duration of its sides. The perimeter formula of some known polygons is given arsenic follows:
- Border of a trigon = a + b + c, where, a, b, and c are the length of its sides.
- Margin of a rectangle = 2 × (length + width)
Before calculating the perimeter of the polygon, we first find exterior whether the tending polygon is a regular polygonal shape or an irregular polygon. After that, the fit formula is used to find the perimeter of the polygonal shape.
Border of Regular Polygons
A polygon that is equilateral and equiangular is known as a regular polygon. Thus, we forecast the border of daily polygons exploitation the formulas associated with apiece polygon. The formulas of some commonly used regular polygons are:
| Names of Regular Polygon | Margin of Regular Polygon |
|---|---|
| Equilateral Triangle | 3 × (length of one side) |
| Square | 4 × (length of one English) |
| Systematic Pentagon | 5 × (length of one side) |
| Regular Hexagon | 6 × (length of one side) |
Consequently, the formula to see the perimeter of a fixture polygon is: Perimeter of regular polygon = (number of sides) × (length of peerless side of meat)
Example: Find the border of a regular hexagon whose each sidelong is 6 inches hourlong.
Solution: Given, the length of one side = 5 inches and the number of sides = 6 (as IT is a hexagon).
Thus, the perimeter of the regular hexagon = (list of sides) × (duration of one position) = (6 × 5) = 30 inches.
Therefore, the circumference of the regular hexagon is 30 inches.
Perimeter of Irregular Polygons
Polygons that do not have equal sides and equal angles are referred to as irregular polygons. Thus, in order to calculate the perimeter of irregular polygons, we add the lengths of all sides of the polygonal shape.
Example: Regain the perimeter of the given polygon.
Result: As we can take in, the given polygon is an irregular polygonal shape since the length of each side is different (AB = 7 units, BC = 8 units, CD = 3 units, and AD = 5 units)
Thus, the perimeter of the irregular polygon will be the sum of the lengths of all its sides.
The perimeter of ABCD = AB + BC + Cd + A.D. ⇒ Circumference of ABCD = (7 + 8 + 3 + 5) = 23 units
Therefore, the perimeter of ABCD is 23 units.
Perimeter of Polygon with Coordinates
The margin of a polygon with coordinates can cost found using the next steps:
- Step 1: Find the distance betwixt all the points using the distance rule, D = \(\sqrt {\left( {x_2 - x_1 } \right)^2 + \left( {y_2 - y_1 } \right)^2 }\), where, \((x_1, y_1)\) and \((x_2, y_2) \) are the coordinates.
- Whole tone 2: Once the dimensions of the polygon are known, we need to find whether the given polygonal shape is a regular polygon or non.
- Step 3: If the polygon is a regular polygonal shape we use the formula, margin of regular polygon = (number of sides) × (length of one side); while if the polygon is an irregular polygonal shape we righteous attention deficit hyperactivity disorder the lengths of all sides of the polygon.
Example: What is the perimeter of the polygon molded aside the coordinates A(0,0), B(0, 3), C(3, 3), and D(3, 0)?
Solution: Happening plotting the coordinates A(0,0), B(0, 3), C(3, 3), and D(3, 0) on an XY plane and joining the dots we get a four-sided polygon as shown below.
In dictate to understand whether it is a regular polygon or non, we need to get hold the length betwixt all the points using the distance formula, D = \(\sqrt {\left( {x_2 - x_1 } \right)^2 + \left( {y_2 - y_1 } \right)^2 }\), where, \((x_1, y_1)\) and \((x_2, y_2) \) are the coordinates. After subbing the values in the formula, the distance of sides Abdominal, BC, CD and DA toilet be calculated as shown below.
- Length of AB = \(\sqrt{({0 - 0})^2 + ({3 - 0})^2}\) = 3 units. This was premeditated with \(x_1\) = 0, \(x_2\) = 0, \( y_1\) = 0, \( y_2\) = 3
- Length of Before Christ = \(\sqrt{({3 - 0})^2 + ({3 - 3})^2}\) = 3 units. This was calculated with \(x_1\) = 0, \(x_2\) = 3, \( y_1\) = 3, \( y_2\) = 3
- Length of CD = \(\sqrt{({3 - 3})^2 + ({0 - 3})^2}\) = 3 units. This was deliberate with \(x_1\) = 3, \(x_2\) = 3, \( y_1\) = 3, \( y_2\) = 0
- Length of District attorney = \(\sqrt{({0 - 3})^2 + ({0 - 0})^2}\) = 3 units. This was calculated with \(x_1\) = 3, \(x_2\) = 0, \( y_1\) = 0, \( y_2\) = 0
Directly, we know that the duration of all sides of the given foursome-sided polygon is the same. This shows that it is a square. Thus, the perimeter of the polygon ABCD (square) can be calculated with the formula, Perimeter = numeral of sides) × (length of same side). Later substituting the values in the formula, we get, border = 4 × 3 = 12 units. Hence, the border of the polygon with coordinates (0,0), (0, 3), (3, 3), and (3, 0) is 12 units.
Perimeter of Polygons Examples
-
Example 1: Find the lacking length FA of the polygonal shape shown to a lower place if the perimeter of polygon is 18.5 units.
Solution: IT can be seen that the given polygon is an irregular polygonal shape. The perimeter of the conferred polygon is 18.5 units. The given lengths of the sides of polygon are AB = 3 units, BC = 4 units, CD = 6 units, First State = 2 units, EF = 1.5 units; and let FA = x units.
Given that, the perimeter of the polygonal shape ABCDEF = 18.5 units
⇒ Border of polygonal shape ABCDEF = AB + BC + CD + DE + EF + FA = 18.5 units ⇒ (3 + 4 + 6 + 2 + 1.5 + x) = 18.5. Frankincense, x = 18.5 - (3 + 4 + 6 + 2 + 1.5) = 2 unitsTherefore, the lacking length FA of the polygon ABCDEF is 2 units.
attend slidego to slide
Breakdown tough concepts through simple visuals.
Math will no longer be a enured subject, especially when you understand the concepts through visualizations with Cuemath.
Book a Free Trial Class
Practice Questions on Margin of Polygons
go to slidego to slide
FAQs connected Perimeter of Polygons
What is the Perimeter of Polygonal shape?
The perimeter of a polygon is defined arsenic the total length of the boundary of the polygonal shape in a two-dimensional plane. The circumference of a polygon is spoken in linear units equal meters, centimeters, inches, feet, etc.
How to Find the Perimeter of a Polygonal shape?
The perimeter of a polygon can be plant by using the following steps:
- Step 1: Find whether the precondition polygon is a regular polygon or not.
- Footfall 2: If information technology is a regular polygon, the perimeter can be calculated using the formula, Perimeter of standing polygon = (number of sides) × (length of one side). In case, if it is an unsystematic polygon, then its margin can be deliberate by adding the lengths of all its sides.
- Step 3: One time the border of the polygon is obtained, we need to mention the unit on with the measure of the perimeter.
What is the Conflict Between the Area and Perimeter of Polygons?
The perimeter of a polygon is the total duration of its boundary, whereas, the area of a polygon is the space involved by the polygon. We can find the perimeter of a polygonal shape by adding the length of all its sides. The area of a polygon is calculated aside exploitation the appropriate formulas or by reducing the polygonal shape into smaller regular polygons. The surface area of a polygonal shape is always expressed in square units, like meter2, cm2, piece the perimeter of a polygon is always open in linear units wish meters, inches, and and then on.
How to Find the Perimeter of Polygons with Vertices?
We can find the perimeter of polygons with given vertices victimization the following stairs:
- Step 1: First, we need to count the distance 'tween all the points using the distance formula, D = \(\sqrt {\left-of-center( {x_2 - x_1 } \right)^2 + \liberal( {y_2 - y_1 } \right)^2 }\), where, \((x_1, y_1)\) and \((x_2, y_2) \) are the coordinates of the vertices.
- Step 2: Once the dimensions of the polygons are familiar, we take to tally whether the given polygonal shape is a regular polygonal shape operating room an irregular polygon.
- Step 3: The perimeter of a regular polygon can beryllium found by using the formula, perimeter of regular polygonal shape = (list of sides) × (distance of one side), whereas, if the polygonal shape is an irregular one, we can simply attention deficit disorder the lengths of all its sides.
How to Find the Perimeter of Regular Polygons?
The perimeter of unconstipated polygons can constitute found using the following steps:
- Ill-use 1: Reckoning the turn of sides of the polygon.
- Step 2: Remark the length of one side.
- Step 3: Use the values obtained in Step 1 and Step out 2 to detect the value of perimeter using the formula, Border of a regular polygonal shape = (list of sides) × (length of one side).
How to Discovery the Perimeter of Irregular Polygons?
In order to count the perimeter of an irregular polygon we use the following stairs:
- Step 1: Note the length of each side of the given polygon.
- Maltreat 2: In one case the length of all the sides is obtained, the perimeter is found by adding all the sides.
Is the Perimeter of a Regular Polygonal shape Directly Relative to the Length of Pull?
Yes, the perimeter of a regular polygon is like a shot proportional to its side length. We know that the perimeter of a regular polygon is calculated by the formula, Perimeter = (number of sides) × (length of one side). Thus, if the length of the sidelong is accumulated, the value of the margin also increases. For example, a square with a side length of 4 units will have a bigger border as compared to a square with a side length of 2 units.
How to Find the Missing Side Length When the Perimeter of Polygonal shape is Given?
We can find the missing incline length when the perimeter of the polygon is given in the following way:
- Dance step 1: Find whether the apt polygon is a regular polygonal shape or non.
- Step 2: If the minded polygon is a regular polygonal shape, past we use the formula, Border of regular polygon = (number of sides) × (length of one side) to find the nonexistent side length. In vitrine, if the given polygonal shape is an irregular polygonal shape, then we supply the lengths of all the given sides and subtract it from the perimeter to get the wanting side.
What is the Formula of the Margin of Polygon?
The formula that is used to calculate the border of a polygon is acerose to understand because 'perimeter' means the join of the length of all its sides and hence, the formula is expressed as, Perimeter = Sum of the sides. If IT is a lax polygon, it way that all the sides are equal. In that eccentric, to seduce things easier, the formula is definite As, Margin = number of sides × length of one side.
How to Find the Perimeter of Polygons with Coordinates?
The perimeter of polygons with coordinates tin can be premeditated by using the following steps.
- First, the distance of the sides of the polygon can be calculated victimisation the outstrip formula. The surrendered coordinates, \((x_1, y_1)\) and \((x_2, y_2) \) are substituted in the space formula, D = \(\sqrt {\left( {x_2 - x_1 } \right)^2 + \left( {y_2 - y_1 } \right)^2 }\).
- After the duration is known, we should chance out if the polygonal shape is a regular polygon operating theater an irregular one. Accordingly, the expression for the margin is wont to figure the perimeter.
- If it is a lawful polygonal shape, the formula that is used is, Perimeter = keep down of sides × length of indefinite side. If information technology is an irregular polygon, then the sides can exist added to find the perimeter using the formula, Border = Summation of the sides.
how to find the missing length of a polygon
Source: https://www.cuemath.com/measurement/perimeter-of-polygon/
