To calculate the perimeter of a quadrilateral, add the measurements of four sides. The perimeter is the distance around a shape. In real-life applications, the perimeter is the fence around a yard or the frame around a picture. The perimeter extends all the way around a two-dimensional shape. A quadrilateral is a polygon that has four sides and four angles. The most common types of quadrilaterals include a square, a rectangle, a rhombus, a trapezoid and a parallelogram.
The Perimeter of a Square and a Rhombus
A square and a rhombus each have four equal sides, but a square has four right angles. The formula for the perimeter is the same for both shapes, and you only need to know the measurement of one side. The formula is 4 x s = perimeter, where s represents the length of one side. If the measurement of one side is 2 inches, multiply 2 by 4. The perimeter is 8 inches.
Perimeter of a Rectangle and Parallelogram
The formulas for the perimeter of a rectangle and parallelogram are the same, because each polygon has two sets of equal sides. The formula is 2(l + w) = perimeter, where l represents the length and w represents the width. Consider a rectangle that has a length of 2 inches and a width of 4 inches. The sum of the length and width is 6. Multiply 6 by 2 and you get a perimeter of 12 inches.
The Perimeter of a Trapezoid
The formula for a trapezoid is a little different, because a trapezoid is a quadrilateral that has two parallel sides of unequal lengths. Two sides have equal lengths to each other. The other two sides have equal lengths to each other, but the length of these two sides differ from the length of the other two sides. Some school desks in classrooms are trapezoids.
The formula is a + b + c + d = perimeter. Each letter corresponds to a different side or base of the shape. For example, suppose that a trapezoid has the edge measurements 2, 3 , 2 and 5 inches. The perimeter is 2 + 3 + 2 + 5, which equals 12 inches.
The Perimeter of an Irregular Quadrilateral
The formula for an irregular quadrilateral -- which is a polygon that has four sides that are of unequal length -- is the same as that of a trapezoid. The formula is a + b + c+ d = perimeter. For example, suppose that a quadrilateral has sides with lengths of 1, 5, 3 and 4 inches. The perimeter equals 1 + 5 + 3 + 4 or 13 inches.
Using Coordinates to Determine Side Length
If you only know the coordinates of the shape, find the side measurements by finding the distance between the points. For instance, find the distance between points A and B for one side and the distance between points B and C for another side. Then, plug the side measurements into the appropriate formula to determine perimeter.
The perimeter of a quadrilateral is the sum of the lengths of all four sides of a quadrilateral.
How to Find the Perimeter of a Quadrilateral
Since a quadrilateral is a plane figure having four sides, the perimeter of a quadrilateral can be obtained by adding the lengths of all four sides.
Following the above procedure, the formula for the perimeter of a quadrilateral is given below:
Find the perimeter of the quadrilateral ABCD with sides 6 cm, 7 cm, 9 cm, and 10 cm.
Solution:
As we know, P = side 1 + side 2 + side 3 + side 4, here side 1 = 6 cm, side 2 = 7 cm, side 3 = 9 cm, and side 4 = 10 cm
= (6 + 7 + 9 + 10) cm
= 32 cm
Calculate the perimeter of the quadrilateral PQRS having sides 4.5 m, 6.5 m, 8.5 m, and 11.5 m.
Solution:
As we know, P = side 1 + side 2 + side 3 + side 4, here side 1 = 4.5 m, side 2 = 6.5 m, side 3 = 8.5 m, and side 4 = 11.5 m
= (4.5 + 6.5 + 8.5 + 11.5) m
= 31 m
Perimeter of Special Quadrilaterals
By using the above formula we can calculate the perimeter of any quadrilateral.
If we are looking to find the perimeter of special quadrilaterals such as rectangle, square, parallelogram, rhombus, trapezoid, and kite, then we can use the formulas given below.