4 Ways To Find Quadrilateral Perimeter Easily

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Quadrilaterals are four-sided polygons that can be found in various shapes and sizes in our daily lives, from the windows of a house to the frames of a picture. Calculating the perimeter of a quadrilateral is an essential skill in mathematics, particularly in geometry. The perimeter of a quadrilateral is the total length of its boundary or the distance around it. In this article, we will explore four easy ways to find the perimeter of a quadrilateral.

What is a Quadrilateral?

A quadrilateral is a polygon with four sides. It can be classified into different types based on its properties, such as a rectangle, square, trapezoid, or rhombus. Each type of quadrilateral has its unique characteristics, but they all have four sides.

Types of Quadrilaterals

• Rectangle: A quadrilateral with four right angles and opposite sides of equal length.
• Square: A quadrilateral with four right angles and all sides of equal length.
• Trapezoid: A quadrilateral with one pair of parallel sides.
• Rhombus: A quadrilateral with all sides of equal length.

Method 1: Finding Perimeter Using the Formula

The formula to find the perimeter of a quadrilateral is the sum of the lengths of all its sides. The formula is:

Perimeter = a + b + c + d

where a, b, c, and d are the lengths of the four sides of the quadrilateral.

For example, if we have a rectangle with sides of length 5 cm, 10 cm, 5 cm, and 10 cm, we can calculate its perimeter as follows:

Perimeter = 5 + 10 + 5 + 10 = 30 cm

Method 2: Finding Perimeter Using the Length of the Sides

If we know the length of the sides of a quadrilateral, we can find its perimeter by adding the lengths of all the sides.

For example, if we have a quadrilateral with sides of length 3 cm, 4 cm, 5 cm, and 6 cm, we can calculate its perimeter as follows:

Perimeter = 3 + 4 + 5 + 6 = 18 cm

How to Find the Length of the Sides

• Use a ruler to measure the length of each side.
• Use a protractor to measure the angles and calculate the length of the sides using trigonometry.
• Use a calculator to calculate the length of the sides using the Pythagorean theorem.

Method 3: Finding Perimeter Using the Diagonals

The diagonals of a quadrilateral are the lines that connect the opposite vertices. If we know the length of the diagonals, we can find the perimeter of the quadrilateral.

For example, if we have a quadrilateral with diagonals of length 10 cm and 15 cm, we can calculate its perimeter as follows:

Perimeter = 2(10 + 15) = 50 cm

How to Find the Length of the Diagonals

• Use a ruler to measure the length of each diagonal.
• Use a protractor to measure the angles and calculate the length of the diagonals using trigonometry.
• Use a calculator to calculate the length of the diagonals using the Pythagorean theorem.

Method 4: Finding Perimeter Using the Coordinates

If we know the coordinates of the vertices of a quadrilateral, we can find its perimeter by calculating the distance between each pair of vertices.

For example, if we have a quadrilateral with vertices at (0, 0), (3, 4), (6, 0), and (3, -4), we can calculate its perimeter as follows:

Perimeter = √((3 - 0)² + (4 - 0)²) + √((6 - 3)² + (0 - 4)²) + √((3 - 6)² + (-4 - 0)²) + √((0 - 3)² + (0 - (-4))²) = √(9 + 16) + √(9 + 16) + √(9 + 16) + √(9 + 16) = √25 + √25 + √25 + √25 = 5 + 5 + 5 + 5 = 20

How to Find the Coordinates of the Vertices

• Use a graph paper to plot the vertices of the quadrilateral.
• Use a calculator to calculate the coordinates of the vertices using the distance formula.

We hope this article has helped you understand the different methods to find the perimeter of a quadrilateral. Whether you are a student or a professional, these methods will come in handy when working with quadrilaterals.

Now, we'd love to hear from you. Have you ever struggled with finding the perimeter of a quadrilateral? What method do you think is the easiest? Share your thoughts in the comments below.