Perimeter of Quadrilateral

In this chapter we will learn the concept and formula of perimeter of quadrilateral with solved examples.

Let us first review the basics of perimeter and quadrilateral concept.

What is Perimeter of Quadrilateral ?

We know that perimeter of any shape is the sum of the boundary of given shape.

Hence, the perimeter of given shape is the total length of its boundary.

Perimeter of Quadrilateral

Quadrilateral is a polygon with 4 sides and angle.

The perimeter of quadrilateral is found by adding all the side length of the given shape.

For example;

Consider the polygon ABCD with 4 sides and angles.

The perimeter is given as;

Perimeter = AB + BC + CD + DA

Hence, we added all the sides of the quadrilateral to get the perimeter.

I hope the concept is clear, let us find perimeter of important shapes.

Perimeter of Important Quadrilaterals

Perimeter of Square

Square is a quadrilateral in which all side length are equal.

Given above is the square ABCD with side length a cm.

Perimeter of square is given as;

Perimeter = AB + BC + CD + DA

Perimeter = a + a + a + a

Perimeter = 4a

Hence, the perimeter of square is 4a.

Perimeter of Rectangle

Rectangle is a quadrilateral in which opposite sides are equal and parallel.

Also in rectangle, all the angle measure 90 degree.

Consider the above rectangle ABCD with length x cm and breadth y cm.

The perimeter of rectangle is given as;

Perimeter = AB + BC + CD + DA

Perimeter = x + y + x + y

Perimeter = 2x + 2y

Hence the perimeter of above rectangle is given as 2x + 2y.

Perimeter of Parallelogram

Parallelogram is a quadrilateral in which opposite sides are parallel and equal.

Given above is the parallelogram ABCD in which;

AB = CD = x cm
AD = BC = y cm

The perimeter of parallelogram is given as;

Perimeter = AB + BC + CD + DA

Perimeter = x + y + x + y

Perimeter = 2x + 2y

Hence, the perimeter of given parallelogram is 2x + 2y.

Perimeter of Rhombus

Rhombus is a quadrilateral in which all sides are equal.

In Rhombus opposite angles are equal and opposite sides are parallel.

Given above is the Rhombus ABCD in which all sides measure x cm.

The perimeter of Rhombus is given as;

Perimeter = AB + BC + CD + DA

Perimeter = x + x + x + x

Perimeter = 4x

Hence, the perimeter of given Rhombus is 4x.

Perimeter of Trapezium

Trapezium is a quadrilateral in which the shape has two parallel sides and two non parallel sides.

Given above is the trapezium in which AB and CD are parallel sides and BC and AD are non parallel sides.

The perimeter of trapezium is given as;

Perimeter = AB + BC + CD + DA

Perimeter = p + q + r + s

Perimeter of Quadrilateral – Solved Problems

(01) Find the perimeter of quadrilateral with sides 10 cm, 13 cm , 16 cm and 19 cm.

Solution
We know that perimeter of quadrilateral is the sum of all sides.

Perimeter = 10 + 13 + 16 + 19

Perimeter = 58 cm

Hence, the perimeter of given quadrilateral is 58 cm.

(02) The length of three sides of quadrilateral is 5 cm, 10 cm and 7 cm. The perimeter of quadrilateral is given as 30 cm. Find the length of fourth side.

Solution
Let the length of fourth side be x cm.

We know that;

Perimeter of quadrilateral = sum of length of 4 sides

30 = 5 + 10 + 7 + x

30 = 22 + x

x = 30 – 22

x = 8 cm

Hence, the fourth side of the quadrilateral measure 8 cm.

(03) Find the perimeter of rhombus of side 3.5 cm.

Solution
In Rhombus, all the side lengths are of equal measurement.

Perimeter of Rhombus = 3.5 + 3.5 + 3.5 + 3.5

Perimeter = 14 cm

Hence, Perimeter of Rhombus measures 14 cm.

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