How to find the area of a rhombus with one diagonal and perimeter

A rhombus is a diamond-shaped quadrilateral with equal sides but unequal angles of inclination between these two sides. It has four sides that are all the same length since it is a quadrilateral. It can be said that the rhombus is a specific type in a parallelogram, if all the sides of the parallelogram are to be equal, it will become a shape known as a rhombus.

By using Diagonals Area of Rhombus:  = (d1 × d2)/2 sq. units.

Where d1 is the length of diagonal 1 and d2 is the length of diagonal 2.

One of the diagonals of a rhombus of an area of 24 sq m is 6m what is the length of its other diagonal?

Solution: 

To find the length of diagonal d2,

Area of Rhombus = 24 sq m 

Length of diagonal d1 = 6 m

Therefore, Area of Rhombus = (d1 × d2)/2 sq. units

24  =  (6 × d2) / 2

24  =  3d2

d2 = 24/3

d2 = 8 m

So the length of diagonal d2 is 8 m.

Sample Questions 

Question 1:  Calculate the area of a rhombus (using diagonal) having diagonals equal to 5 cm and 4 cm.

Solution: 

Given,

Length of diagonal 1 (d1) = 5 cm

Length of diagonal 2 (d2) = 4 cm

Now,

Area of Rhombus (A) = 1/2 d1 × d2

= 1/2  × 5 × 4

= 1/2 × 20 

= 10 cm2 

Question 2: Find the diagonal of a rhombus if its area is 100 cm2 and the length measure of the longest diagonal is 10 cm.

Solution: 

Given: Area of rhombus = 100 cm2 and Diagonal d1 = 10 cm.

Hence, Area of the rhombus formula, A = (d1 × d2)/2 square units, we get

100 = (10 × d2)/2

100 = 10 d2 / 2

Or 5d2 = 100

d2 = 20

Therefore, the Length of another diagonal d2 is 20 cm.

Question 3: Calculate the area of a rhombus whose diagonals are of the lengths 15 cm and 4 cm?

Solution:

Given: Diagonal d1 = 15 cm

Diagonal d2 = 4 cm

Area of a rhombus, A = (d1 × d2) / 2

= (15 × 4) / 2

= 60/2

= 30 cm2

Hence, the area of a rhombus is 30 cm2.

Question 4:  Find the area of the rhombus where the side of the rhombus is 4 cm and one of the interior angles is 30°.

Solution:

Given,

Side length = 4 cm

Interior angle = 30°

Using Trigonometry , Area of rhombus = (side)2 Sin(30°)

= 42 × sin(30°)

= 16 × (1/2)

= 8 cm2

So the area of Rhombus is 8 cm2. 

Question 5: Find the perimeter of a rhombus whose side is 6 cm.

Solution: 

Given side s = 6 cm

Therefore, Perimeter of Rhombus = 4 × s

So, Perimeter (P) = 4 × 6 cm 

= 24 cm

Question 6: One of the diagonals of a rhombus of area 30 sq m is 6m what is the length of its other diagonal?

Solution: 

To find the length of diagonal d2,

Area of Rhombus = 30 sq m

Length of diagonal d1 = 6 m

Therefore, Area of Rhombus  = (d1 × d2)/2 sq. units

30 = (6 × d2) / 2

30  =  3d2

d2 = 30/3

d2 = 10 m

So the length of diagonal d2 is 10 m.

Question 7: Find the height of the rhombus whose area is 200 m² and the perimeter is 100 m?

Solution:

Given, the perimeter of the rhombus = 120 m

So, side of rhombus = 100/4 

= 25 m

We know that the area of Rhombus = b × h

Therefore the height is, 200 = 25 × h

h = 200 /25

h = 8

Therefore, the height of the rhombus is 8 m.

A rhombus has 4 edges of equal length. If it has perimeter of 40cm, then each length would be

#{40"cm"}/4 = 10"cm"#

Divide the rhombus into 4 right-angle triangle by cutting along the 2 diagonals.

Each right-angle triangle will have a hypotenuse of 10cm and one other edge with length

#{12"cm"}/2 = 6"cm"#

Use Pythagoras Theorem to find the length of the remaining edge.

#sqrt{(10"cm")^2 - (6"cm")^2} = 8 "cm"#

Now find the area of the triangle.

#1/2 xx 6 "cm" xx 8"cm" = 24 "cm"^2#

Since the original rhombus was made up of four such triangles, the area of the rhombus would be

#24 "cm"^2 xx 4 = 96 "cm"^2#

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A rhombus is a parallelogram with four congruent sides. It does not have to have right angles.[1] There are three formulas for finding the area of a rhombus. Just follow these steps if you want to know how to do it.

1. 

   1

   Find the length of each diagonal. The diagonals of a rhombus are the lines that connect the opposite vertices (corners) in the center of the shape. The diagonals of a rhombus are perpendicular and form four right triangles through their intersection.[2]

   • Let's say the diagonals are 6 cm. and 8 cm. long.

2. 

   2

   Multiply the length of the diagonals. Just write down the length of the diagonals and multiply them. In this case, 6 cm x 8 cm = 48 cm2. Don't forget to square the units since you're working in square units.[3]

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3. 

   3

   Divide the result by 2. Since 6 cm x 8 cm = 48 cm2, just divide the result by 2. 48 cm2/2 = 24 cm2. The area of the rhombus is 24 cm2.[4]

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1. 

   1

   Find the base and the height.[5] You can also think of this as multiplying the altitude of the rhombus with the length of the side of the rhombus. Let's say the height of the rhombus is 7 cm and the base is 10 cm.

2. 

   2

   Multiply the base and height. Once you know the base and height of the rhombus, all you have to do to find the area of the shape is to multiply them. So, 10 cm x 7 cm = 70 cm2. The area of the rhombus is 70 cm2.[6]

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1. 

   1

   Square the length of any side. A rhombus has four equal sides, so it doesn't matter which side you choose. Let's say the side is 2 cm long. 2 cm x 2 cm = 4 cm2.[7]

2. 

   2

   Multiply it by the sine of one of the angles. It doesn't matter which angle you choose. Let's say one of the angles is 33 degrees. Just multiply sine (33) by 4 cm2 to get the area of the rhombus. (2 cm)2 x sine (33) = 4 cm2 x 0.55 = 2.2 cm2. The area of the rhombus is 2.2 cm2.[8]

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Add New Question

• Question

  How do I find the perimeter of a rhombus?

  

  Perimeter = sum of all sides. The rhombus has equal sides, so its perimeter = side x 4.

• Question

  How can I find the height of a rhombus?

  

  In a rhombus, the diagonals bisect and are perpendicular, meaning that inside the rhombus there are four right-angle triangles, with side lengths half that of the diagonals, use the pythagoran theorem to find the hypotenuses a² + b² = c² Now we have the base, given any of the angles inside the rhombus, we can find all of them because they are corresponding and all add up to 360 degrees, once we have all of the angles, another two identical triangles appear. we only have to use one of these as they are identical. Now we have the hypotenuse and an angle of this triangle so using trigonometry we can find the adjacent side which is the height of the rhombus.

• Question

  How do I determine the perimeter given one diagonal and the area?

  

  Use the Pythagorean theorem to find the sides and then find the perimeter.

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Article SummaryX

A rhombus is a shape with four equal sides, each of which is parallel to the opposite side. While a square is a type of rhombus, they can also be diamond-shaped, with angles of greater or less than 90° at each corner. There are several easy ways to find the area of a diamond-shaped rhombus. One is to measure the rhombus diagonally from corner to corner, each way. For instance, let’s say your rhombus measures 10 cm across lengthwise and 6 cm across widthwise. Once you find the length of each diagonal, multiply the lengths together. In this case, 10 cm x 6 cm = 60 cm. Finally, divide the result by 2. Don’t forget to square your units when you write the result, since you’re measuring the area. 60/2 = 30, so our rhombus has an area of 30 cm squared. Another simple method is to multiply the base length of the rhombus by its height. Measure the width of the bottom line of the rhombus, then take a perpendicular measurement from the base to the opposite line at the top. Multiply the measurements together to find the area. For instance, if a rhombus is 12 cm long at the base and has a height of 8 cm, the area of the rhombus would be 96 cm squared. If you only know the length of one side of the rhombus and one of the angles, you can still figure out the area using trigonometry. To do this, square the length of the known side, then multiply the result by the sine of one of the angles. For instance, if the rhombus has one side with a length of 6 cm, and you know it contains a 45° angle, the area would be 36 cm squared x sin(45°), or approximately 30.63 cm squared. If you want to learn how to use trigonometry to find the area of the rhombus, keep reading the article!

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