Prepare For Rhombus

Introduction

A rhombus is actually just a special type of parallelogram. Area calculations can be applied to them also. A rhombus has four equal sides and its diagonals bisect each other at right angles.In geometry, a rhombus or rhomb is a quadrilateral whose four sides all have the same length. The rhombus is often called a diamond, after the diamonds suit in playing cards, or a lozenge, though the latter sometimes refers specifically to a rhombus with a 45° angle.Every rhombus has two diagonals connecting opposite pairs of vertices and two pairs of parallel sides. Using congruent triangles, one can prove that the rhombus is symmetric across each of these diagonals.

General representation of rhombus

Where:

A,B,C,D are four sides

d1 and d2 are the diagonals.

Properties

1. Opposite angles of a rhombus have equal measure.

2. The two diagonals of a rhombus are perpendicular.

3. Diagonals of a rhombus bisect each other at right angles.

4. Diagonals of a rhombus bisect opposite angles

 5. Square is special case of rhombus.

6.Any two consecutive internal angles are supplementary : they add up to 180 degrees.

angle A + angle B = 180 degrees

angle B + angle C = 180 degrees

angle C + angle D = 180 degrees

angle D + angle A = 180 degrees

 

Formulae

 

Area of rhombus

Area of rhombus is identified by two methods:

Base and height method:The perpendicular distance from the chosen base to the opposite side.

Area=ba

Where:b is the length of the base

             a is the altitude(Height)

Diagonal method:The area is half the product of the diagonals.

Area=d1d2/2

Where:d1 is the length of a diagonal

             d2 is the length of the other diagonal

Trignomentry

 Area=s2sina

Where:s is the length of any side

             a is any interior angle

             sin is the sine function

Perimeter:It is the total distance around the outside.

Perimeter=4s

Where:S is the length of any one side

 

 

 

Solved problem

 

1) Find the area of rhombus when x=24 and y=12 cm?

Given: X=24cm and Y=12cm

Area=xy/2

24x12=288

Area=288/2=144cm2