Perimeter of Quadrilateral
The perimeter of quadrilateral is just the sum of all its side lengths. A quadrilateral is a polygon with four sides. A quadrilateral can be regular or irregular. A regular quadrilateral has all its side lengths equal. An irregular quadrilateral is not a regular quadrilateral (i.e., it has at least two sides that are not equal). There are 6 specific types of quadrilaterals.
Here, we will learn the formula of finding the perimeter of quadrilateral in detail along with a few solved examples.
|1.||What Is Perimeter of Quadrilateral?|
|2.||Perimeter of Quadrilateral Formula|
|3.||Perimeter Formulas of Different Types of Quadrilaterals|
|4.||Perimeter of Quadrilateral With Circle Inside|
|5.||FAQs on Perimeter of Quadrilateral|
What Is Perimeter of Quadrilateral?
The perimeter of a quadrilateral is nothing but the length of its boundary. i.e., if we attach all the four side lengths 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 the quadrilateral is same as that of its side. i.e., it is measured in m, in, cm, etc.
Perimeter of Quadrilateral Formula
In the previous section, we learned the definition of the perimeter of a quadrilateral. From that, the perimeter of a quadrilateral can be just obtained by adding all its side lengths. i.e., the perimeter of a quadrilateral ABCD is,
Perimeter = AB + BC + CD + DA
Perimeter Formulas of Different Types of Quadrilaterals
We already have 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. Then 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 have to find the perimeter of a square with only one side length (assume that its side length is x) given, we need to recollect one of the properties of the square that all its side lengths are equal. Then each of the 4 sides of the square is x and hence its perimeter is x + x + x + x = 4x. In the same way, we can derive the perimeter formulas of all of the 6 specific types of quadrilateral mentioned.
Perimeter of Quadrilateral With Circle Inside
Sometimes, a quadrilateral with some missing sides has a circle (circumscribed quadrilateral) inside it. In that cases, we use a 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 below.
Example: Find the perimeter of the following quadrilateral.
Using the above property of tangents,
PT = PU = 5 in
QV = QU = 2 in
RW = RV = 3 in
ST = SW = 4 in
Now the perimeter of the quadrilateral is,
PQ + QR + RS + SP
= (PU + QU) + (QV + RV) + (RQ + SW) + (ST + PT)
= (5 + 2) + (2 + 3) + (3 + 4) + (4 + 5)
= 28 in
Therefore, the perimeter of the given quadrilateral = 28 in.
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" for finding the perimeter of a cyclic quadrilateral (a quadrilateral that is inscribed in a circle) as well.
Solved Examples on Perimeter of Quadrilateral
Example 1: Find the perimeter of a kite whose adjacent sides are 7 units and 13 units using the perimeter of the quadrilateral formula.
We know that a kite has two pairs of equal adjacent sides. So the sides of the given kite are 7 units, 7 units, 13 units, and 13 units.
Thus the perimeter of the given kite is,
7 + 7 + 13 + 13 = 40 units.
Answer: The perimeter of the given kite = 40 units.
Example 2: Find the perimeter of the following quadrilateral ABCD.
The perimeter of the given quadrilateral ABCD can be obtained by adding all its sides. But the length of CD is NOT given. Let us find it first.
CD2 = BC2 + BD2 = 62 + 82 = 36 + 64 =100
CD = √100 = 10
Thus, the perimeter of the given quadrilateral is,
AB + BC + CD + DA = 15 + 6 + 10 + 10 = 41 in.
Answer: The perimeter of ABCD = 41 in.
FAQs on Perimeter of Quadrilateral
What Is Meant By the Perimeter of Quadrilateral?
The perimeter of a quadrilateral is equal to the sum of its four sides. i.e., the perimeter of a quadrilateral ABCD is AB + BC + CD + DA.
What Is the Formula of Perimeter of Quadrilateral?
Since the perimeter of a quadrilateral is just the sum of all its sides, the perimeter of a quadrilateral with sides a, b, c, and d is a + b + c + d. In fact, no particular formula is needed to find the perimeter of a quadrilateral, instead, we can just add all the sides.
How To Find the Perimeter of a Quadrilateral With a Missing Side?
A missing side of a quadrilateral can be found either by using the properties of quadrilaterals (or) the properties of triangles. Once all the missing sides are found, we can find the perimeter of the quadrilateral just by adding all the side lengths.
How To Find the Perimeter of Quadrilateral With Circle Inside?
Any two tangents drawn from a point to some points on a circle are always of equal lengths. We use this property of tangents to find the missing side lengths of a quadrilateral. Once all missing sides are found, we can find the perimeter of the quadrilateral just by adding all four sides.
How To Find the Perimeter of Quadrilateral That Is Inscribed in a Circle?
When a quadrilateral is inscribed in a circle, it is called a cyclic quadrilateral. To find the missing sides of a cyclic quadrilateral, we just apply the property of the tangent of a circle that says any two tangents of a circle drawn from the same point are of the same lengths. After finding the missing sides, we add all four side lengths to find the perimeter.
How To Find the Perimeter of a Quadrilateral With Coordinates?
When the coordinates of a quadrilateral's vertices are given, we first find its side lengths by using the distance formula. Then, we just all the four side lengths to find its perimeter.
How To Find the Perimeter of a Quadrilateral on Graph?
To find the perimeter of a quadrilateral that is on a graph,
- Find the coordinates of the vertices from the graph.
- Apply the distance formula to find the side lengths of the quadrilateral.
- Just add all the side lengths and the sum gives the perimeter of the quadrilateral.