Area of Rhombus

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) of a rhombus bisect each other at right angles. Rhombus formed from an isosceles triangle and its shadow reflected on the base as the axis of symmetry. Isosceles triangle ABC is reflected to the side of the base AC, so it appears his shadow ACD. ACD is congruent with the ABC. 

The properties of a rhombus as follows :

1. The length of its four sides equal in length 

     and Opposite sides are parallel.

• AB = BC = CD = AD
• AB // DC dan AD // BC

2. Both rhombus diagonal bisect each other 

    the same length and intersect 

    perpendicularly.

3. Opposite angles equal.

• ∠BAD =  ∠BCD
• ∠ABC =  ∠ADC
• ∠BAE =  ∠DAE =  ∠BCE = ∠ DCE
• ∠ADE =  ∠CDE =  ∠ABE =  ∠CBE

4. Both diagonal are  axis of symmetry.

• Diagonal AC ┘└ BD
• Panjang AE = EC
• Panjang DE = EB

Area of Rhombus :

Area =  ½ x d1 x d2
Based on rhombus area can be found each diagonal.

• d1  = 2A/d2
• d2 = 2A/d1

Example :

1. A rhombus has diagonal 1 = 15 cm and diagonal 2 = 20 cm. What is the area ?

    Area = di x d2

             = 15 x 20

             = 300 cm

2. A rhombus has 300 cm area and one of the diagonal is 30 cm. What is the other diagonal ?

     d1 = 2A/d2

          = 2(300)/30

          = 600/30

          = 20 cm

3.  A rhombus has 187 cm area and one of the diagonal is 17 cm. What is the other diagonal ?

     d2 = 2A/d1

          = 2(187)/17

          = 374/17

          = 22 cm