The most commonly used formulas to calculate the rhombus area are listed here. Students are advised to know when to use those formulas to get the accurate output.

1. If you know side length of rhombus and height, then use this formula.

Area of a rhombus = a x h

Where,

a is the length of side of a rhombus

h is the height of the rhombus

2. If you have the lengths of two diagonals, then make use of the below provided formula.

Area = ½ × e × f

Where,

e, f are the lengths of diagonals of rhombus.

3. If you know side length, angle of a rhombus, then

Rhombus area = a² x sin(α)

Where,

a is the length of side of a rhombus

α is the angle between any sides of a rhombus.

Below given are the some steps which are useful for you to solve the area of a rhombus questions by knowing any value of it easily. Look at them and follow when you are unable to solve the questions.

1. When you have side, height

• Get the required data such as length of the side and height of the rhombus from your questions.
• Multiply those values to find the result i.e area.

2. When you have diagonals length

• Note down the length of major and minor diagonals of rhombus from the question.
• Multiply the diagonal values.
• Divide the product of diagonals by 2 to obtain the area.

3. If you have side length and angle

• Obtain the length of side and angle between the sides of rhombus from the question.
• Square the side length and find the trigonometry sin of angle.
• Multiply those two values to find the rhombus area.

Example 1: Calculate the area of a rhombus having diagonals equal to 10 cm and 8 cm?

Solution:

Given that,

Diagonals of rhombus e = 10 cm, f = 8 cm

Rhombus Area = ½ × e × f

substitute the diagonal values in the formula

area = ½ × 10 × 8

= ½ × 80

= 40

∴ Area of a rhombus having diagonals equal to 10 cm and 8 cm is 40 cm².

Example 2: Calculate area of a rhombus if the length of its side is 14 cm and one of its angle A is 40 degrees?

Solution:

Given that,

The length of side of rhombus a = 14 cm

Angle = 40 degrees

Area of a Rhombus = a² x sin(α)

Put the values in the formula.

Area = 14² x sin(40°)

= 14 x 14 x 0.64279

= 125.98

∴ Area of a rhombus having side length 14 cm and angle 40 degrees is 125.98 cm².

Example 3: Find the area of a rhombus if its base is 7 cm and height is 5 cm?

Solution:

Given that,

Base length a = 7 cm

Height h = 5 cm

Area of a rhombus = a x h

= 7 x 5

= 35

∴ Rhombus area is 35 cm².

Areavolumecalculator.com is an geometry calculator tool where you will learn, practice, and discover several shapes area, surface area, perimeter, volume, etc.

1. What is rhombus?

Rhombus is a quadrilateral whose opposite sides are parallel and in equal length. Also, the opposite angles of rhombus measures the equal quantity and its diagonals are perpendicular to one other.

2. How do you measure the area of an rhombus?

The simple methods are using diagonals, using base and height and using trigonometry. The rhombus area can be defines as the half of the product of diagonals or product of base length and height. You have to square the base length and apply sine function of angle to get the area value.

3. What is the formula to find the perimeter of rhombus?

Perimeter of rhombus p = 4a. where a is the length of side of a rhombus.

4. One of the diagonals of rhombus is 3 cms more than other. If its area is 14 cm², find diagonals length?

e = x, f = x+3

area = ½ × e × f = ½ × x x (x+3)

14 = (x² + 3x) / 2

x² + 2x = 28

x² + 2x - 28 = 0

(x + 7) (x - 4) = 0

So, e = 4 cm, f = 7 cm