The perimeter of quadrilateral is the total length of its boundary. A quadrilateral is a four-sided polygon that can be regular or irregular. In a regular quadrilateral, all the sides are equal in length and all the angles are of equal measure, whereas, in an irregular quadrilateral, the sides and angles are not equal. There are 6 specific types of quadrilaterals - Square, rectangle, parallelogram, rhombus, kite, and trapezoid. Let us learn how to find the perimeter of quadrilateral in this page.

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 1 What is Perimeter of a Quadrilateral? 2 Perimeter of Quadrilateral Formula 3 Perimeter Formulas of Different Types of Quadrilaterals 4 Perimeter of Quadrilateral With Inscribed Circle 5 FAQs on Perimeter of Quadrilateral

## What is Perimeter of a Quadrilateral?

The perimeter of a quadrilateral is the length of its boundary, i.e., if we join all the four sides of a quadrilateral to form a single line segment, the length of the resultant line segment is called its perimeter. Thus, the unit of the perimeter of a quadrilateral is the same as that of its side, i.e., it is measured in linear units like meters, inches, centimeters, etc.

We know that the perimeter of a quadrilateral can be obtained by adding all its side lengths. This can be expressed by a simple formula. For example, the formula for the perimeter of a quadrilateral ABCD can be expressed as,

Perimeter = AB + BC + CD + DA

## Perimeter Formulas of Different Types of Quadrilaterals

We have already seen that there are 6 specific types of quadrilaterals, which are, square, rectangle, parallelogram, rhombus, kite, and trapezoid. Though the perimeter of a quadrilateral is the sum of all its sides, sometimes, all the side lengths might not have been given. In such cases, we need to recollect the properties of quadrilaterals with respect to sides, in order to obtain the side lengths that are not given. For example, if we need to find the perimeter of a square with only one side length given, we need to recollect one of the properties of the square, that all its side lengths are equal. So, if we assume one side of the square to be x, its perimeter will be x + x + x + x = 4x. In the same way, we can derive the perimeter formulas of all of the 6 specific types of quadrilaterals. Observe the following figure to see the different formulas that are used for calculating the perimeter of quadrilaterals.

## Perimeter of Quadrilateral With Inscribed Circle

Sometimes, a quadrilateral has a circle inside it. This is termed as a circumscribed quadrilateral or a quadrilateral with an inscribed circle. In such cases, we use the property of the tangent of a circle which says "any two tangents drawn to a circle from a point are of equal lengths". We will see how to find the perimeter of a circumscribed quadrilateral (or) the perimeter of a quadrilateral with a circle inside it using the example given below.

Example: Find the perimeter of the following quadrilateral.

Solution:

Using the property of tangents - 'Any two tangents drawn to a circle from a point are of equal lengths', let us find the perimeter of quadrilateral with an inscribed circle.

PT = PU = 5 inches

QV = QU = 2 inches

RW = RV = 3 inches

ST = SW = 4 inches

Now the perimeter of the quadrilateral is,

PQ + QR + RS + SP

= (PU + UQ) + (QV + VR) + (RW + WS) + (ST + TP)

= (5 + 2) + (2 + 3) + (3 + 4) + (4 + 5)

= 28 inches

Therefore, the perimeter of the given quadrilateral = 28 inches.

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Note: We can use the same property of tangents of a circle "two tangents drawn to a circle from a point are of equal lengths" to find the perimeter of a cyclic quadrilateral (a quadrilateral that is inscribed in a circle) as well.