Perimeter of Quadrilateral: Easy Formulas & Examples!
The study of geometry offers fundamental tools for understanding shapes, and the perimeter, a critical measurement, defines the total distance around any two-dimensional figure. The perimeter of quadrilateral, a specific type of polygon, plays a significant role in diverse applications, from calculating fencing requirements for a garden (a practical application often explored in surveying) to designing structures with optimal material usage (a key consideration in architecture). Euclid’s Elements provides foundational postulates and theorems that underpin our understanding of these calculations; therefore mastering how to compute the perimeter of quadrilateral equips you with valuable skills applicable across many fields.
Image taken from the YouTube channel Sheena Doria , from the video titled PERIMETER OF QUADRILATERALS | GRADE 4 .
Understanding the Perimeter of Quadrilateral: Formulas and Examples
This article provides a clear and comprehensive guide to understanding and calculating the perimeter of a quadrilateral. We will explore different types of quadrilaterals, their specific properties, and how these properties influence the perimeter calculation.
What is a Quadrilateral?
A quadrilateral is a two-dimensional geometric shape with four sides and four angles. The word "quadrilateral" comes from the Latin words "quadri" (meaning four) and "latus" (meaning side). Therefore, any closed shape formed by four straight lines is considered a quadrilateral.
Defining the "Perimeter of Quadrilateral"
The perimeter of quadrilateral refers to the total distance around the outer edge of the shape. It is found by adding the lengths of all four sides. This simple concept is key to understanding how to work with various types of quadrilaterals.
General Formula for the Perimeter of Quadrilateral
The most basic formula to calculate the perimeter of quadrilateral is:
Perimeter = Side 1 + Side 2 + Side 3 + Side 4
Where:
- Side 1, Side 2, Side 3, and Side 4 are the lengths of the four sides of the quadrilateral.
This formula applies to all quadrilaterals, regardless of their shape or properties.
Specific Types of Quadrilaterals and Perimeter Calculations
While the general formula works for all quadrilaterals, certain types have specific properties that can sometimes simplify the calculation of the perimeter of quadrilateral.
Squares
A square is a quadrilateral with four equal sides and four right angles.
-
Formula: Perimeter = 4 * Side
Where:
- Side represents the length of one side of the square.
Rectangles
A rectangle is a quadrilateral with two pairs of equal sides and four right angles.
-
Formula: Perimeter = 2 * (Length + Width)
Where:
- Length represents the length of the longer side.
- Width represents the length of the shorter side.
Parallelograms
A parallelogram is a quadrilateral with two pairs of parallel sides. Opposite sides are equal in length, and opposite angles are equal.
-
Formula: Perimeter = 2 * (Side A + Side B)
Where:
- Side A and Side B represent the lengths of the two adjacent (non-parallel) sides.
Rhombuses
A rhombus is a quadrilateral with four equal sides and two pairs of equal angles.
-
Formula: Perimeter = 4 * Side
Where:
- Side represents the length of one side of the rhombus (since all sides are equal).
Trapezoids (or Trapeziums)
A trapezoid is a quadrilateral with at least one pair of parallel sides.
-
Formula: Perimeter = Side 1 + Side 2 + Side 3 + Side 4 (all sides might be different lengths)
Where:
- Side 1, Side 2, Side 3, and Side 4 represent the lengths of all four sides. There is no simplification because the sides may all have different lengths.
Kites
A kite is a quadrilateral with two pairs of adjacent sides that are equal in length.
-
Formula: Perimeter = 2 * (Side A + Side B)
Where:
- Side A and Side B represent the lengths of the two different pairs of equal sides.
Examples of Calculating the Perimeter of Quadrilateral
Let’s look at some practical examples:
-
Square: A square has a side length of 5 cm. Calculate the perimeter of quadrilateral.
- Perimeter = 4 Side = 4 5 cm = 20 cm
-
Rectangle: A rectangle has a length of 8 cm and a width of 3 cm. Find the perimeter of quadrilateral.
- Perimeter = 2 (Length + Width) = 2 (8 cm + 3 cm) = 2 * 11 cm = 22 cm
-
Parallelogram: A parallelogram has sides of lengths 6 cm and 4 cm. Calculate the perimeter of quadrilateral.
- Perimeter = 2 (Side A + Side B) = 2 (6 cm + 4 cm) = 2 * 10 cm = 20 cm
-
Trapezoid: A trapezoid has sides of lengths 3 cm, 5 cm, 7 cm, and 4 cm. Find the perimeter of quadrilateral.
- Perimeter = 3 cm + 5 cm + 7 cm + 4 cm = 19 cm
-
Rhombus: A rhombus has a side length of 7cm. Calculate the perimeter of quadrilateral.
- Perimeter = 4 Side = 4 7cm = 28cm
Summary Table of Perimeter Formulas
| Quadrilateral Type | Formula for Perimeter of Quadrilateral |
|---|---|
| Square | 4 * Side |
| Rectangle | 2 * (Length + Width) |
| Parallelogram | 2 * (Side A + Side B) |
| Rhombus | 4 * Side |
| Trapezoid | Side 1 + Side 2 + Side 3 + Side 4 |
| Kite | 2 * (Side A + Side B) |
FAQs: Perimeter of Quadrilateral
Got questions about finding the perimeter of quadrilaterals? Here are some frequently asked questions to help you understand the concepts better.
What is the simplest way to find the perimeter of any quadrilateral?
The easiest way to find the perimeter of any quadrilateral is to simply add the lengths of all four sides together. This works regardless of the quadrilateral’s shape (square, rectangle, trapezoid, etc.). So, perimeter of quadrilateral = side1 + side2 + side3 + side4.
Does the formula for the perimeter of a quadrilateral change depending on its type?
No, the fundamental formula remains the same: add the lengths of all sides. However, for specific quadrilaterals like squares or rhombuses where all sides are equal, you can use a shortcut: Perimeter = 4 * side length. This is just a quicker way of adding the sides in cases where they are identical. The general rule always applies to finding the perimeter of quadrilateral.
What if I only know the lengths of some sides of a quadrilateral?
If you’re missing the length of one or more sides, you’ll need additional information. This could be angle measures, diagonal lengths, or relationships between the sides. Use geometric principles like the Pythagorean theorem (for right triangles within the quadrilateral) or properties of specific quadrilateral types to deduce the missing side lengths before calculating the perimeter of quadrilateral.
Can the perimeter of a quadrilateral be used to find its area?
Generally, no. Knowing the perimeter of a quadrilateral alone is not enough to determine its area. You need additional information like the lengths of the diagonals, angles between sides, or the height of the quadrilateral to calculate its area. A long, skinny rectangle and a square could have the same perimeter but different areas; therefore, more details than just the perimeter of quadrilateral is required.
So, there you have it! Calculating the perimeter of quadrilateral is a breeze once you get the hang of it. Go forth and conquer those shapes!
