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Formula to Find Height of a Rhombus

A parallelogram in which all four sides are equals called a rhombus. In rhombus ABCD shown in the figure AB = BC = CD = DA and AB is parallel to CD and BC is parallel to AD. 

A Parallelogram

Properties of Rhombus:
         All the sides are equal.
         Opposite angles are equal
         Diagonal bisect each other at an angle of 90º

Area of Rhombus:
Rhombus is similar to a parallelogram. The sides of a rhombus remains same.
The area can be found by :

Area of Rhombus

  • When Diagonals are given:
                     The area of rhombus (A) = $\frac{d_{1}d_{2}}{2}$
  • When base and height of Rhombus is known:

A Rhombus

                      The area of rhombus (A) = b x h 
                      where b is base and h is height of  a rhombus.

Height of a Rhombus:
Height of Rhombus can be found when the area and base of rhombus is known.

Formula for height of rhombus:
We have area of rhombus A = base x height

           $\frac{Area}{base}$ = height

Example Problems:

           1. Find the height of Rhombus when the area is 54 cm2 and height 6 cm.

Solution:  We have area of Rhombus = base x height

                         Height = $\frac{Area}{base}$

                                   = $\frac{54}{6}$

                                   =  9 cm.

                         Height of rhombus is 9 cm.

            2. The diagonal of Rhombus are 6 cm and 8 cm with base 4 cm. Find the height of the rhombus.

  Solution:  Given the diagonals of rhombus  d1 and d2 are 6 cm and 8 cm.

                  Area of rhombus when diagonals are known: A = $\frac{d_{1}d_{2}}{2}$

                                                                    = $\frac{6*8}{2}$

                                                                    = $\frac{48}{2}$ = 24 cm2

                 Height of Rhombus ; h = $\frac{Area}{base}$

                                                  = $\frac{24}{4}$

                                                  = 6 cm.

                Height of rhombus is 6 cm.

Best Results From Yahoo Answers Youtube

From Yahoo Answers

Question:I have to find the height of a rhombus. Then find the perimeter and area. 1. Rhombus (5in sides) 90' angle at height and base is 3in. 2. Rhombus (1cm sides) 90' angle at height and base is 0.6cm. How can I figure this out. Is there a formula to find the height?

Answers:The side of the rhombus is the hypotenuse of a right triangle. One leg is 3, the other is the height. You can either recognize the 3-4-5 pythagorean triple or use the Pythagorean theorem to calculate the height: 5^2 = 3^2 + h^2 25 = 9 + h^2 16 = h^2 h = 4 Height is 4in for part 2: (also a 3-4-5) 1^2 = 0.6^2 + h^2 1 = 0.36 + h^2 0.64 = h^2 h = 0.8 cm

Question:Please help, I need maths help! I need to know the formula to calculate the perpendicular height of a triangle. thanks Okay, I need to know the FORMULA to calculate the height of a triangle WITHOUT A CALCULATOR. WHAT IS THE FORMULA PLEASE!?

Answers:Area=(base x height)/2 to find the heght you can change the subject and get for height: height=2xArea/base

Question:I am doing homework late at night and i have school tomorrow and i forgot how to find the height of a triangle.. =/ too fun of a weekend=[

Answers:well you have to be given certain information. for example: area = (base x height) / 2 so to solve for height you go height = 2area / base thats your height.

Question:Is this correct? find the area of a triangle with base 10cm and corresponding height 4cm A = 1/2bh 10 * 4 = 40/2 = 20 Answer: 20 ________________________________________________________ Find the area of a rhombus with diagonals 4m and 12m. A = (1/2) d1 (d2) A = 5(4) (12) = 2*12 = 24m^2 Answer: 24m^2 ___________________________________________________ Find the area of a trapezoid with bases 5in and 11in and height 3in. = 1/2 * 3 3 (5+11) = 3*16 =48 48/2 = 24 Answer: 24 _____________________________________________________ Find the height of a trapezoid with bases 6ft and 10ft and area 32sq ft. 32 = 1/2h (6+10) 32 = 8h 32/8 = 8h/8 = 4 = h Answer: 4ft _______________________________________________ Find the area of a regular hexagon with side 2 sqrt3 cm and apothem 3cm. 1/2 2sqrt 3 = 3 Answer: 3

Answers:You forgot the units on your first, third and fifth answer. Other than that, they are correct! Nice work!

From Youtube

Rhombus Geometry Problem :www.gdawgenterprises.com This short video shows the working out of the 2009 Exit level math TAKS problem 29. It asks for the height of a rhombus. The problem is attempted using geometry sense and also by using the special right triangle expressions from the TAKS formula chart.

Math Made Easy: Finding the Area of a Rhombus :In this video, I show you how to find the area of a rhombus using a formula.