MATHS
QUERY

We have learnt what a quadrilateral is and different types of a quadrilateral in the chapter Quadrilateral and its Types. 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.

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.

Example

Example of perimeter calculation is how long a runner has to run around a rectangular shape playground to finish one round. The runner has to go around the boundary of the rectangle and cover up all the sides. So, the distance covered by him will be equal to the sum of all sides of the rectangle, which is called the perimeter.

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

Example

Example of area calculation is how much area one has to paint on one side surface of a rectangular shape wooden board. If we need to paint both sides of rectangular board, then it will be two surfaces to paint that will make two areas of board to be painted.

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

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)

Formula

Perimeter of parallelogram = 2(a + b)

Area of a parallelogram is calculated by multiplying its length of base and height h.

So, area of parallelogram = base × height = b × h

Formula

Area of parallelogram = b × h

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)

Formula

Perimeter of rectangle = 2(l + b)

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

= l × b

Formula

Area of square = l × b

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

Formula

Perimeter of square = 4l

Area of a square is calculated by multiplying its length and breadth.

So, area of square = length × breadth = l × l = l^{2}

Formula

Area of square = l^{2}

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 $\sqrt{\mathrm{d12}+d}$_{2}^{2}

Formula

Perimeter of rhombus = 4a

Perimeter of rhombus = 2 $\sqrt{\mathrm{d12}+d}$_{2}^{2
}

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 d_{1} × d_{2}

Formula

Area of rhombus = a × h

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

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

Formula

Perimeter of trapezium = a + b + c + d

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

= $\frac{1}{2}$ (a + b) × height

Formula

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