Perimeter and Area of Quadrilaterals

Introduction

We have learnt what a quadrilateral is and different types of a quadrilateral in the chapter Quadrilateral and Types of Quadrilateral. As the number of sides of a quadrilateral are always fixed i.e. four, so, the types of Quadrilateral are classified based on how the length of four sides vary and how inclined the sides are.

In this chapter, we will learn about the measurements that can be done for a quadrilateral. Perimeter and the area calculations are the mostly used measurements on a quadrilateral.

Perimeter

The perimeter of any plane figure is the total length of its boundary. In other words, we can say perimeter is how long the boundary of a quadrilateral is and is calculated by adding up the length of all sides of a quadrilateral. The perimeter is measured by the same units as of length i.e. millimeter, centimeter, meter, kilometer etc.

Area

The area of any plane figure is the amount of surface enclosed by its sides. Let’s understand it by an example:

Let’s have a look at how to calculate the area and perimeter of various types of quadrilaterals.

Perimeter of parallelogram

Parallelogram with two parallel sides a, b and height h

Perimeter of a parallelogram is calculated by adding up the length of all sides.
The parallelogram in above figure has two parallel sides a, b and height h. We can write it as:
Perimeter = a + b + a + b = 2a + 2b = 2(a + b)

Area of parallelogram

Area of a parallelogram is calculated by multiplying its length of base and height h.
So, area of parallelogram = base × height = b × h

Perimeter of rectangle

Rectangle with length l and breadth b

Perimeter of a rectangle is calculated by adding up the length of all sides. The rectangle in above figure has length l and breadth b. Therefore, the perimeter will be the sum of length of its four sides.

We can write it as:

Perimeter = l + b + l + b = 2l + 2b = 2(l + b)

Area of rectangle

Area of a rectangle is calculated by multiplying its length and breadth. So, area of square = length × breadth
= l × b

Perimeter of square

Square with length l of its four sides

Perimeter of a square is calculated by adding up the length of all sides.

The square in above figure has length l of its four sides. Therefore, the perimeter will be the sum of length of its four sides. We can write it as:
Perimeter = l + l + l + l = 4l
Perimeter of the square can also be calculated by multiplying 4 with length l of the square. So, perimeter can also be calculated as:
Perimeter = 4 × l = 4l

Area of square

Area of a square is calculated by multiplying its length and breadth.
So, area of square = length × breadth = l × l = l²

Perimeter of rhombus

Rhombus with length l and breadth b

Perimeter of a rhombus is calculated by adding up the length of all sides. The rhombus in above figure has length a of its all sides because the length of all sides of a rhombus are always equal. Therefore, the perimeter will be the sum of length of its four sides. We can write it as:
Perimeter = a + a + a + a = 4a
Perimeter of the rhombus can also be calculated by multiplying 4 with length a. So, perimeter can also be calculated as:
Perimeter = 4 × a = 4a

Rhombus with diagonals

Perimeter of the rhombus is also calculated using the length of two diagonals.
Perimeter = 2 $\sqrt{\mathrm{d₁²}+d}$₂²

Area of rhombus

Area of a rhombus is calculated by multiplying its length of base and height h.
So, area of rhombus = base × height = a × h
Area of the rhombus is also calculated using the length of two diagonals.

Area of rhombus = $\frac{1}{2}$X d₁ × d₂

Perimeter of trapezium

Trapezium with sides a, b, c, d and height h

Perimeter of a trapezium is calculated by adding up the length of all sides.
The trapezium in the above figure has sides a, b, c, d and height h. We can write it as:
Perimeter = a + b + c + d

Area of trapezium

Area of trapezium = $\frac{1}{2}$ (sum of parallel sides) × h
= $\frac{1}{2}$ (a + b) × height