Calculation of Perimeter and Area of Quadrilaterals

The chapter Quadrilateral and Types of Quadrilateral explains what a quadrilateral is and different types of the quadrilateral. 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 varies and how inclined the sides are.

This chapter will teach about calculations of the measurement of area and perimeter of a quadrilateral.

Perimeter of 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 of perimeter

A runner runs around a rectangular shaped 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 will be equal to the perimeter of the playground.

Area of quadrilateral

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

Example of area of quadrilateral

A rectangular shaped wooden board is an example of a quadrilateral. To paint on its surface of one side, the area to be painted will be equal to the area of the quadrilateral.
To paint both sides of the rectangular board, there will be two surfaces to paint and that will make two areas of board to be painted or two areas of the quadrilateral.

Perimeter of parallelogram

The perimeter of a parallelogram is calculated by adding up the length of all sides.

Parallelogram with two parallel sides a, b and height h

The parallelogram in the figure has two parallel sides a, b and height h.
Its perimeter is equal to
a + b + a + b
= 2a + 2b
= 2(a + b)

Perimeter of parallelogram with length of parallel sides a and b

Formula

Perimeter of parallelogram = 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

Formula

Area of parallelogram = b × h

Perimeter of rectangle

The perimeter of a rectangle is calculated by adding up the length of all sides. Therefore, also, the perimeter can be calculated as the sum of length of its four sides.

Rectangle with length l and breadth b

The rectangle in the figure has length l and breadth b. ∴ Perimeter = l + b + l + b
= 2l + 2b
= 2(l + b)

Perimeter of rectangle of sides of length l and b

Formula

Perimeter of rectangle = 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

Formula

Area of square = l × b

Perimeter of square

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

Square with length l of its four sides

The square in the figure has length l of its four sides.
∴ Perimeter = l + l + l + l
= 4l

Perimeter of square with length of sides equal to l

Formula

Perimeter of square = 4l

The perimeter of a square can also be calculated by multiplying 4 with length l of the square. So, perimeter of a square with sides of length l is:
= 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

Formula

Area of square = l²

Perimeter of rhombus

The perimeter of a rhombus is calculated by adding up the length of all sides, because the length of all sides of a rhombus are always equal.

Rhombus with length of sides = a

The rhombus in the figure has sides length = a
∴ Perimeter of rhombus= a + a + a + a
= 4a
Or perimeter of the rhombus can also be calculated by multiplying 4 with length a.
∴ also, perimeter of rhombus = 4 × a
= 4a

Perimeter of rhombus of length of four sides a

Formula

Perimeter of rhombus = 4a

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

Formula

Area of rhombus = a × h

Area and perimeter of rhombus with diagonals

Perimeter and area of a rhombus can also be calculated using the length of two diagonals.

Perimeter of rhombus with diagonals = $2 \sqrt{d_{1}^{2} + d_{2}^{2}}$
Area of rhombus with diagonals = $\frac{1}{2} \times d_{1} \times d_{2}$

Area and perimeter of rhombus with length of diagonals

Perimeter of trapezium

The perimeter of a trapezium is calculated by adding up the length of all sides.

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

The trapezium in the figure has sides a, b, c, d and height h.
∴ Perimeter of trapezium = a + b + c + d

Perimeter of trapezium with sides length a, b, c, d

Formula

Perimeter of trapezium = a + b + c + d

Area of trapezium

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

Perimeter of trapezium with sides length a, b, c, d and height h

Formula

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

Solved Examples

1) Find the perimeter of the square whose length of each side is 10 cm.

Length of side of square = 10 cm
Perimeter of square = 4 × side
= 4 × 10
= 40 cm

2) Find the length of the sides of a square whose perimeter is 80 cm.

Perimeter of square = 80 cm
Perimeter of square = 4 × side
80 = 4 × side
$\frac{80}{4}$ = side
20 = side
∴ length of side = 20 cm

3) Find the perimeter of a rectangle whose length is 10 m and breadth is 15 m.

Length of rectangle = 10 m
Breadth of rectangle = 15 m
Perimeter of rectangle = 2(l + b)
= 2(10 + 15)
= 2(25)
= 50
∴ Perimeter = 50 m

4) Find the length of a rectangular park if its perimeter is 100 m and breadth is 30 m.

Perimeter of rectangular park = 100 m
Breadth = 30 m
Let length of rectangular park = l
Perimeter of rectangle = 2(l + b)
100 = 2(l + 30)
$\frac{100}{2}$ = l + 30
50 = l + 30
50 - 30 = l
20 = l
∴ length of rectangular park = 20 m

5) Find the cost of fencing a square shaped park which has a length of each of its sides as 25 m. The cost of fencing is $10 per metre.

Length of each side of park = 25 m
Perimeter of square = 4 × side
∴ Perimeter of park = 4 × 25
= 100 m
Cost of fencing per meter = $10
∴ Cost of fencing of 100 m = 10 × 100
= $1000

6) A boy and a girl jog on the ground. The boy jogs around a rectangular shaped ground whose length and breadth are 50 m and 70 m respectively. The girl jogs around a square shaped ground whose length of each side is 50 m. Find out who covered the more distance among the boy and girl.

Distance covered by the girl:
Length of each side of ground = 50 m
Perimeter of square = 4 × side
∴ Perimeter of square shaped ground = 4 × 50
= 200 m
Distance covered by the boy:
Length of ground = 50 m
Breadth of ground = 70 m
Perimeter of rectangle = 2(l + b)
∴ Perimeter of rectangular ground = 2(50 + 70)
= 2(120)
= 240 m
The boy covered 240 m and the girl covered 200 m. So, the boy covered more than the girl by 240 - 200 = 40 m.

7) Find the area of a square whose length of each side is 8 cm.

Side of square = 8 cm
Area of square = side × side
= 8 × 8
= 64 cm²

8) Find the area of a rectangle whose length is 40 cm and breadth is 20 cm.

Length of rectangle = 40 cm
Breadth of rectangle = 20 cm
Area of rectangle = l × b
= 40 × 20
= 800 cm²

9) The area of a rectangle 200 cm². Find the breadth of the rectangle if its length is 10 cm.

Length of rectangle = 10 cm
Area of rectangle = 200 cm²
Also, Area of rectangle = l × b
200 = 10 × b
$\frac{200}{10}$ = b
20 = b
∴ breadth of rectangle = 20 cm

10) The length and breadth of a room are 10 m and 20 m respectively. Find the cost of flooring a room at the rate of $10 per square meter.

Length of room = 10 m
Breadth of room = 20 m
Area of rectangular room = l × b
= 10 × 20
= 200 m²
Cost of flooring per m² = $10
∴ Cost of flooring of 200 m² = 10 × 200
= $2000

Fill in Blanks Worksheet

Blanks - 1

Area of rectangle = ___ × breadth.
Area of rhombus = $\frac{1}{2} \times d_{1} \times____$
Perimeter of square = ___ × side.
Perimeter of rectangle = ___ (l + b).
Perimeter of rhombus = 4 × ___.
Area of parallelogram = ___ × height.
Area of trapezium = $\frac{1}{2} (sum of parallel sides) \times____$
Area of square of side 12 cm is ___cm².
Area of the rectangle of 10 cm × 12 cm is ___cm².
Perimeter of the rhombus of each side 4 cm is ___ cm.

Help box

120

side

height

144

length

base

d₂

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Word Problems Worksheets

Word Problems - 2

Questions on calculation of perimeter of quadrilaterals.

Find the perimeter of a square whose side is 10 cm.
Find the perimeter of a rectangle whose length is 20 cm and breadth is 12 cm.
What will be the breadth of a rectangle whose length is 25 cm and perimeter is 90 cm.
What will be the length of the side of the square whose perimeter is 80 cm.
An athlete runs 3 rounds of a squared shape path whose side is 15 cm. Find the total distance covered by him.

Questions on calculation of area of quadrilaterals.

The length of the rectangle is 15 cm and breadth i s 14 cm, find the area of the rectangle.
Find the area of a square whose side is 24 cm.
How many times does the new area become of the original area of a square if the length of the side of the square is doubled?
The floor of a rectangular room is 60 cm × 50 cm. The floor will be fitted with tiles of size 15 cm × 10 cm. Calculate the total number of tiles required to fit into the room.
Area of a square is 576 cm². Calculate length of side and perimeter of the square.

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Multiple Choice Questions Worksheet

MCQ - 1

1) What is the distance covered by an athlete in one round of a squared shape path, which has length of each of its sides as 40 m?