This document provides information about various types of quadrilaterals (four-sided shapes). It defines quadrilateral, rectangle, rhombus, square, parallelogram, and trapezium. For each shape, it describes the key properties like side lengths, angle measures, and how to calculate the area and perimeter. The goal is to explain these geometric concepts in a clear, step-by-step manner to make mathematics more accessible and enjoyable for students.

1. 1
ASHA PHILIP. MSc

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PREFACE
I t is common belief that mathematics is a
dull and difficult subject. It has been dreaded by many
children. The problem lies in the traditional way the
subject is treated and taught. It has, in fact, the potential to
be enjoyed and appreciated the way music and paintings
are appreciated.
Mathematics forms an integral part of everyday
life. We have to teach it with freshness and variety to
make it meaningfully applicable to life. This is a humble
attempt at it. This text book is designed to meet the
everyday requirements of students at school and the
general readers of mathematics. I humbly dedicate this
book to all students and teachers.
Suggestions for improvement are welcome.
The author.

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CONTENTS
1. Quadrilateral
2. Rectangle
3. Rhombus
4. Square
5. Parallelogram
6. Trapezium
7. Reference

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QUADRILATERALS
1.1 INTRODUCTION
In Euclidean plane geometry,
a quadrilateral is a polygon with four sides (or edges) and four
vertices or corners. Sometimes, the term quadrangle is used, by
analogy withtriangle, and sometimes tetragon for consistency
with pentagon (5-sided), hexagon (6-sided) and so on.
The origin of the word "quadrilateral" is the two Latin
words quadri, a variant of four, and latus, meaning "side".
Quadrilaterals are simple (not self-intersecting)
or complex (self-intersecting), also called crossed. Simple
quadrilaterals are either convex or concave.
The interior angles of a simple (and planar)
quadrilateral ABCD add up to 360 degrees of arc, that is
Any four-sided shape is a Quadrilateral. But the sides have to
be straight, and it has to be 2-dimensional.

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1. 2 PROPERTIES
 Four sides (edges)
 Four vertices (corners)
 The interior angles add up to 360 degrees:
1. 3 TYPES OF QUADRILATERAL
 Rectangle
 Rhombus
 Square
 Parallelogram
 Trapezium

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2. RECTANGLE
2.1 DEFINITION
The Rectangle
means "right
angle"
and
show equal
sides
A rectangle is a four-sided shape where every angle is a right
angle (90°).
Also opposite sides are parallel and of equal length.
2.2 DIAGONALS OF RECTANGLE
A rectangle has two diagonals. Each one is a line segment drawn
between the opposite vertices(corners) of the rectangle. The
diagonals have the following properties:
 The two diagonals are congruent (same length). In the
figure above, click 'show both diagonals', then drag the
orange dot at any vertex of the rectangle and convince
yourself this is so.

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 Each diagonal bisects the other. In other words, the point
where the diagonals intersect(cross), divides each diagonal
into two equal parts
 Each diagonal divides the rectangle into two congruent
right triangles. Because the triangles are congruent, they
have the same area, and each triangle has half the area of
the rectangle
2.3 MEASUREMENTS
Area of a rectangle = length * breadth.
Perimeter of a rectangle =2( l + b)
d the length of the diagonal if we know the width and height of
the rectangle.
Then,
where:
w is the width of the rectangle
h is the height of the rectangle

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3. RHOMBUS
3.1 DEFINITION
A rhombus is a four-sided shape where all sides have equal
length.
Also opposite sides are parallel and opposite angles are equal.
Another interesting thing is that the diagonals (dashed lines in
second figure) meet in the middle at a right angle. In other
words they "bisect" (cut in half) each other at right angles.
A rhombus is sometimes called a rhomb or a diamond.
3.2 PROPERTIES OF RHOMBUS
Base Any side can be considered a base. Choose any
one you like. If used to calculate the area (see
below) the corresponding altitude must be used.
In the figure above one of the four possible
bases has been chosen.
Altitude The altitude of a rhombus is
the perpendicular distance from the base to the
opposite side.

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3.2 MEASUREMENTS
Area There are several ways to find the area of a
rhombus. The most common is (base × altitude).
Area of a rhombus =
푑1푑2
2
; where 푑1 , 푑2 are
the diagonals of the rhombus.
Perimeter Distance around the rhombus. The sum of its
side lengths.

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4. SQUARE
4.1 DEFINITION
The Square
means "right
angle"
show equal
sides
A square has equal sides and every angle is a right angle (90°)
Also opposite sides are parallel.
A square also fits the definition of a rectangle (all angles are
90°), and a rhombus (all sides are equal length).
4.1 PROPERTIES
Vertex The vertex (plural: vertices) is a corner of the
square. Every square has four vertices
Diagonals Each diagonal of a square is the perpendicular
bisector of the other. That is, each cuts the other
into two equal parts, and they cross and right angles

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(90°).
The length of each diagonal is
s√2
where s is the length of any one side.
4 . 2 MEASUREMENTS.
Area: Like most quadrilaterals, the area is the length of
one side times the perpendicular height. So in a
square this is simply:
area = s2
where s is the length of one side..
Perimeter: The distance around the square. All four sides are by
definition the same length, so the perimeter is four
times the length of one side, or:
perimeter = 4s
where s is the length of one side

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5. PARALLELOGRAM
5.1 DEFINITION
The Parallelogram
A parallelogram has opposite sides parallel and equal in length.
Also opposite angles are equal (angles "a" are the same, and
angles "b" are the same). .
A parallelogram is a quadrilateral with opposite sides parallel. It
is the "parent" of some other quadrilaterals, which are obtained
by adding restrictions of various kinds:
 A rectangle is a parallelogram but with all four interior
angles fixed at 90°
 A rhombus is a parallelogram but with all four sides equal
in length
 A square is a parallelogram but with all sides equal in
length and all interior angles 90°
A quadrilateral is a parallelogram if:
1. Both pairs of opposite sides are parallel. (By definition).
Or:

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2. Both pairs of opposite sides are congruent. If they are
congruent, they must also be parallel. Or:
3. One pair of opposite sides are congruent and parallel. Then,
the other pair must also be parallel.
5.2 PROPERTIES OF A PARALLELOGRAM
These facts and properties are true for parallelograms and the
descendant shapes: square, rectangle and rhombus.
Base Any side can be considered a base. Choose any
one you like. If used to calculate the area (see
below) the corresponding altitude must be used.
In the figure above, one of the four possible
bases and its corresponding altitude has been
chosen.
Altitude
(height)
The altitude (or height) of a parallelogram is
the perpendicular distance from the base to the
opposite side (which may have to be extended).
In the figure above, the altitude corresponding
to the base CD is shown.
Area The area of a parallelogram can be found by
multiplying a base by the corresponding
altitude.
Perimeter The distance around the parallelogram. The sum
of its sides.

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Opposite sides Opposite sides are congruent (equal in length)
and parallel. As you reshape the parallelogram
at the top of the page, note how the opposite
sides are always the same length.
Diagonals Each diagonal cuts the other diagonal into two
equal parts, as in the diagram below.
See Diagonals of a parallelogram for an
interactive demonstration of this.
Interior angles
1. Opposite angles are equal as can be seen
below.
2. Consecutive angles are always
supplementary (add to 180°)

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6. TRAPEZIUM
6.1 DEFENITION
The Trapezium
In a trapezium only one pair of opposite sides are parallel.
6.2 PROPERTIES OF TRAPEZIUM
Base One of the parallel sides. Every trapezoid has two
bases..
Leg The sides AC and BD above are called the legs of
the trapezoid, and are usually not parallel, although
they could be. Every trapezoid has two legs.
Altitude The altitude of a trapezoid is
the perpendicular distance from one base to the
other. (One base may need to be extended).
Median The median of a trapezoid is a line joining the
midpoints of the two legs.

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6.3 MEASUREMENTS
Area The usual way to calculate the area is the average
base length times altitude.
Perimeter The distance a round the trapezoid. The sum of its
side lengths.
REFERENCE:
1) https://www.google.co.in/search?q=G&oq=g&aqs=chr
ome.0.69i59j69i60j69i59j69i60l3.1419j0j7&sourceid=
chrome&es_sm=93&ie=UTF-8#q=quadrilatelas
2) https://www.google.co.in/search?q=geometrical+figur
es
&oq=geometrical+figures&aqs=chrome..69i57.8179j0
j9&sourceid=chrome&es_sm=93&ie=UTF-8