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Quadrilateral: Overview and Examples
Any four points that don't lie on the same line make a quadrilateral; this shape goes by different names based on its form. A quadrilateral is a flat geometric figure with four sides and four corners. Understanding quadrilaterals is essential for various exams like SSC, Railways, AAI, and academic tests. A quadrilateral encompasses shapes like parallelograms, rectangles, squares, rhombuses, trapeziums, and kites, each with unique properties and formulas. These geometric concepts are crucial for competitive exams and academic studies.
Quadrilateral
In geometry, a quadrilateral is a shape with four sides, four angles, and four vertices. It's formed by connecting four points where any three points are not in a straight line. Several types of quadrilaterals exist, including a square, rectangle, parallelogram, rhombus, trapezium, and kite. We'll explore each type in the sections ahead.Types of Quadrilaterals
The term Quadrilateral originates from a Latin term, where Quadra signifies four and Latus means sides. A quadrilateral can have four sides that are either the same or different. Examples of quadrilaterals include rectangle, square, trapezoid, and kite, which typically exhibit a four-sided structure.Various types of quadrilaterals are elaborated upon below:
Parallelogram
Definition: A quadrilateral with two pairs of opposite sides that are parallel and equal in length.
Properties:- Opposite sides are parallel (AB || CD, BC || AD).
- Opposite sides are equal in length (AB = CD, BC = AD).
- Diagonals bisect each other.
- The sum of any two adjacent angles is 180 degrees (∠A + ∠B = 180°, ∠B + ∠C = 180°, etc.).
Rectangle
Definition: A parallelogram where each angle measures 90 degrees.
Properties:- Opposite sides are parallel (AB || CD, BC || AD).
- Opposite sides are equal in length (AB = CD, BC = AD).
- All angles are equal to 90 degrees (∠A = ∠B = ∠C = ∠D = 90°).
- Diagonals bisect each other and are equal in length.
Square
Definition: A parallelogram with all sides equal and each angle measuring 90 degrees.
Properties:- All sides are equal in length (AB = BC = CD = DA).
- Opposite sides are parallel (AB || CD, BC || AD).
- All angles are equal to 90 degrees (∠A = ∠B = ∠C = ∠D = 90°).
- Diagonals bisect each other at right angles and are equal in length.
Rhombus
Definition: A parallelogram where all sides are equal, and the diagonals bisect each other at right angles.
Properties:- All sides are equal in length (AB = BC = CD = DA).
- Opposite sides are parallel (AB || CD, BC || AD).
- Opposite angles are equal.
- Diagonals bisect each other perpendicularly.
Trapezium
Definition: A quadrilateral with only one pair of opposite sides that are parallel.
- Only one pair of opposite sides are parallel (AB || CD).
- The non-parallel sides are called the legs of the trapezium.
- The diagonals do not bisect each other in the same ratio.
Kite
Definition: A quadrilateral with two pairs of adjacent sides that are equal in length.
Properties:
- Two pairs of adjacent sides are equal (AB = AD, BC = CD).
- The diagonals intersect at right angles.
- One of the diagonals bisects the other.
Quadrilateral Formula
- Shapes: We previously talked about square, rectangle, parallelogram, rhombus, trapezium, and kite with a detailed illustration.
- Formulas: Let's now understand the fundamental equations connected to these shapes. Area and perimeter represent the basic formulas for different four-sided figures. The following are the formulas:
- Area: The space inside a shape.
- Perimeter: The total length of the boundary of a shape.
Perimeter of Quadrilateral
- The perimeter refers to the total distance around the edge of any flat shape.
- In a four-sided shape (quadrilateral), the perimeter is the sum of all four side lengths.
- Various types of quadrilaterals have different perimeters.
Note: The perimeter is the total distance around the edge of a 2D shape, like a square or rectangle. For a quadrilateral, which is a shape with four sides, the perimeter is the sum of all four side lengths. Different types of quadrilaterals have different perimeters based on their side measurements.
| Shape | Formula for Perimeter |
| Parallellogram |
|
| Rectangle |
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| Square |
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| Rhombus |
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| Trapezium |
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| Kite |
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Area of Quadrilateral
The area of a four-sided shape is the total space it takes up. Here are the area formulas for different shapes:
- Square: All sides are equal. Area = side x side
- Parallelogram: Opposite sides are parallel. Area = base x height
- Rectangle: Opposite sides are equal and all angles are 90 degrees. Area = length x width
- Rhombus: All sides are equal, opposite angles are equal. Area = (diagonal1 x diagonal2) / 2
- Trapezium: One pair of parallel sides. Area = 0.5 x (sum of parallel sides) x height
- Kite: Two pairs of adjacent sides are equal. Area = 0.5 x (diagonal1 x diagonal2)
| Shape | Area |
| Parallelogram | b × h (base × height) |
| Rectangle | Length × Breadth ( L × B) |
| Square | a2 (side length squared) |
| Rhombus | 1/2×d1×d2 (where length of two diagonals of the is d1 and d2) |
| Trapezium | 1/2×(Addition of lengths of parallel sides)×h (where, 'h' represents the height) |
| Kite | 1/2×Diagonal1×Diagonal2 |
Sides and Angles of Quadrilaterals
Learn about key facts on sides and angles of parallelogram, rectangle, square, rhombus, and trapezium.- Opposite sides run alongside each other and look the same with lines from corner to corner cutting each other into two.
- The angles have different measurements, but the opposite angles are of the same size.
| Shape | Sides | Angles |
| Parallelogram |
|
|
| Rectangle |
|
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| Square |
|
|
| Rhombus |
|
|
| Trapezium |
| - |
| Isosceles trapezium |
| - |
Properties of Quadrilaterals
Common Properties of Quadrilaterals:- Quadrilaterals have four sides.
- Quadrilaterals have four vertices.
- Quadrilaterals have two diagonals.
- The total of all interior angles is 360 degrees.
- Rectangle
- Parallelogram
- Rhombus
- Square
- Trapezoid
- Kite
| Shape | Properties |
| Square |
|
| Rectangle |
|
| Rhombus |
|
| Parallelogram |
|
Trapezium |
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Kite |
|
Solved Examples on Quadrilateral
- A polygon is a flat shape with many sides. For instance, a shape with three sides is called a 3-gon, and one with four sides is known as a 4-gon.
- This article focuses on quadrilaterals, which are polygons with four sides. The total angles inside a quadrilateral add up to 360 degrees.
- Here are some solved examples of quadrilaterals.
Example 1 : Obtain the perimeter of the quadrilateral with sides 6 cm, 7 cm, 8 cm and 13 cm.
Example 2 : If the two diagonals of a kite are of length 22 cm and 6 cm then what is the respective area.
Example 3 :Determine the perimeter of the parallelogram whose opposite sides are 13 cm and 6 cm respectively.
Example 4 : What is the base of a rectangle having an area of 72 square units and the height is 8 units.
The document Quadrilateral: Overview and Examples is a part of the SSC CGL Course Quantitative Aptitude for SSC CGL.
All you need of SSC CGL at this link: SSC CGL
FAQs on Quadrilateral: Overview and Examples
| 1. What are the different types of quadrilaterals and how do I identify them? |  |
Ans. A quadrilateral is a polygon with four sides, four angles, and four vertices. Main types include parallelograms (opposite sides parallel), trapezoids (one pair of parallel sides), rectangles (right angles), squares (equal sides and angles), rhombuses (equal sides), and kites (two pairs of adjacent equal sides). Each type has distinct properties that help identify them during SSC CGL exams.
| 2. How do I calculate the area and perimeter of different quadrilaterals for SSC CGL? | |
Ans. Area and perimeter formulas vary by quadrilateral type. Rectangles use length × width for area and 2(l+w) for perimeter. Squares use side² for area and 4×side for perimeter. Parallelograms use base × height for area. Trapezoids use ½(sum of parallel sides)×height. Rhombuses use ½×d₁×d₂ where d₁ and d₂ are diagonals. Mastering these formulas is essential for solving quantitative aptitude problems quickly.
| 3. What's the difference between a parallelogram and a trapezoid in geometry? | |
Ans. A parallelogram has both pairs of opposite sides parallel and equal, while a trapezoid has only one pair of parallel sides. In parallelograms, opposite angles are equal and diagonals bisect each other. Trapezoids don't have these properties. Understanding this distinction helps students correctly apply properties and formulas when solving quadrilateral-based SSC CGL questions involving angles and sides.
| 4. Why do the angles of a quadrilateral always add up to 360 degrees? | |
Ans. The angle sum property states that interior angles of any quadrilateral total 360 degrees because a quadrilateral can be divided into two triangles, and each triangle's angles sum to 180 degrees. This fundamental concept applies to all quadrilateral types-squares, rectangles, rhombuses, kites, and irregular shapes. Students should memorise this property as it's frequently tested in SSC CGL quantitative sections.
| 5. How can I distinguish between a rhombus and a square using their properties? | |
Ans. Both rhombuses and squares have all four sides equal, making them special parallelograms. The key difference: squares have all angles measuring 90 degrees, while rhombuses have opposite angles equal but not necessarily 90 degrees. Additionally, square diagonals are equal in length, whereas rhombus diagonals are unequal. Recognising these distinctions helps solve geometry problems accurately in competitive exams and ensures correct application of area formulas.
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