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Special quadrilaterals in Geometry

Updated: Jun 22, 2021

Dear Secondary Math students, Math Lobby will be going through the topic Special quadrilaterals in Geometry today. Let’s begin!

In this note, you will learn:


1) Types of special quadrilaterals (parallelogram, trapezium and rhombus) and their unique properties

2) Formulae of the special quadrilaterals

1) Types of special quadrilaterals (parallelogram, trapezium and rhombus)


From our previous article, we talked about the various types of triangles and its unique properties. If you haven’t checked that out, you can do so right here, 1) Congruent Triangles and 2) Similar Triangles! Today, we will be taking it up a notch and talk about four-sided figures and its’ unique properties. Let’s begin!

By mathematical definition, a quadrilateral is a four-sided 2-dimensional figure that has a sum of its interior angles to be 360°. However, the quadrilaterals we will be talking about today is more than just that, let’s take a look at the special types of quadrilaterals below:




There are three special quadrilaterals we will be focusing on today:

Parallelogram – which has equal opposite angles and opposite sides, which are parallel, diagonals bisect each other and adjacent angles add up to 180°


Rhombus – which opposite angles and ALL sides are equal, which opposites are parallel, diagonals bisect each other PERPENDICULARLY and adjacent angles add up to 180°.


Trapezium – which only one pair of opposite sides are parallel to each other.


Test yourself!


Grab a piece of paper and cover your notes, then draw out the respective shapes and pen down their qualities, uncover your notes and see if you’re right!

Formulae of the special quadrilaterals

Now that you know the unique properties of the special quadrilaterals, let’s take a look at their formulae next!


Area of parallelogram = Length x Height

Perimeter of parallelogram = 2 x (Length + Height)

Area of a rhombus = ½ x d1 x d2, where d1 and d2 are the lengths of the two diagonals

Perimeter of rhombus = 4b, where b is a side of the rhombus

Area of trapezium = ½ x (a+b) x h, where a and b are length of the parallel sides

Perimeter of trapezium = Sum of the lengths of all the sides

Question Time!

Parallelogram


1. DEFG is a parallelogram in which ∠D = 130°. Find the measure of each of the angles ∠E, ∠F and ∠G.


2. Two adjacent angles of a parallelogram are in the ratio 3 : 5. Find the measure of each of its angles.


3. Two adjacent angles of a parallelogram are (3x - 8)° and (2x + 14)°. Find the value of x and hence find the measure of each of its angles.


4. The perimeter of a parallelogram is 140 cm. If one of the sides is longer than the other by 10 cm, find the length of each of its sides.

Rhombus


1. The size of the obtuse angle of a rhombus is twice the size of its acute angle. The side length of the rhombus is equal to 10m. Find the area of the rhombus.


2. The lengths of the diagonals of a rhombus are 20 and 48 meters. Find the perimeter of the rhombus.


3. The perimeter of a rhombus is 120m and one of its diagonals has a length of 40m. Find the area of the rhombus.

Trapezium


1. Find the area of a trapezium whose parallel sides are 32 cm and 18 cm and the distance between them is 20 cm.


2. The area of a trapezium is 1160 cm². If the lengths of its parallel sides are 72.8 cm and 43.2 cm, find the distance between them.


3. The area of a trapezium is 864cm². Its parallel sides are in the ratio 7 : 13 and the perpendicular distance between them is 12 cm. Find the length of each of the parallel sides.


4. The area of a trapezium is 1742 cm² and the distance between its parallel sides is 24 cm. If one of the parallel sides is 96 cm, find the other.

And that’s all we have for today, students! Math Lobby hopes that after this article, all of you would have a better understanding of the special quadrilaterals that exist in this world and their amazing unique properties! If you have any questions or queries, please feel free to contact Math Lobby on our Facebook page, Instagram or on the Math Lobby website itself!


As always: Work hard, stay motivated and we wish all students a successful and enjoyable journey with Math Lobby!



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