What is the area of a rhombus in CM² whose side is 10 cm and the smaller diagonal is 12 cm?

The rhombus area calculator is an excellent tool to determine the area of a rhombus, as well as its perimeter and other characteristics: diagonals, angles, side length, and height.

Have a look at many ways you can find the diamond area: given diagonals of a rhombus, using base and height, side, and any chosen angle... Are you still wondering how to find the area of a rhombus or rhombus perimeter? Check the rhombus area formulas below, or just experiment with the tool.

A rhombus is a simple quadrilateral with all sides equal. The other names are an equilateral quadrilateral or a diamond (like the one from playing cards ♢).

The fundamental properties of a rhombus are:

• The two diagonals of a rhombus are perpendicular and bisect each other;
• Its diagonals bisect opposite angles; and
• Opposite angles have equal measure.

Every rhombus is a parallelogram and a kite.

There are three useful formulas for calculation of the area of the rhombus:

1. Knowing base and height:

   area = base × height

2. Knowing the diagonals of a rhombus:

   area = (e × f)/2

3. Knowing the side s and any (!) angle:

   area = s² × sin(angle)

Why can we use any angle in the last rhombus area formula? Because we know that two adjacent angles are supplementary, and sin(angle) = sin(180° - angle).

There are other variations of those equations (e.g., calculating the area given height and angle), but they are only simple trigonometric transformations of those three most popular rhombus area formulas.

Finding the rhombus perimeter is trivial if we know the side length – it's 4 × a. But what if we know only the diagonals of a rhombus? Let's check:

1. We know that diagonals are perpendicular and bisect each other. So the rhombus is nothing else than four congruent triangles, with legs equal to e/2 and f/2.

2. All we need to do is find the hypotenuse of the triangle. You can use here the right triangle calculator or Pythagorean theorem calculator.

3. Multiply by 4 the obtained hypotenuse value. It's your rhombus perimeter!

Also, you can use this formula:

• perimeter = 4 × √(e/2)² - (f/2)²)

Or just type the lengths of the diagonals into the rhombus area calculator!

Are you still pretty unsure how to use the calculator? Let's show its potential with a simple example:

1. Type the first given value you have. Let's assume its side = 10 in.

2. Type the second given value. For example, an angle equal to 30°.

3. Wow! The rhombus area calculator displays all the other values – area, height, perimeter, angle, and diagonals. Impressive, isn't it?

Our tool is really flexible – if it's possible to calculate, it will do it. Usually, two given values are enough. Give it a try!

The answer is yes to both questions. Every square is a rhombus, as for a rhombus, the only necessary condition is that it needs to have all sides of equal length. As you know perfectly well, a square needs to have all sides equal and all four equal angles, so it fulfills the conditions to be a rhombus.

Similarly, a rhombus is a parallelogram, as any shape needs to have two pairs of parallel sides to be a parallelogram – and the rhombus has them. So the rhombus is always a parallelogram, but a parallelogram is a rhombus only in a special case – for a parallelogram with four sides of equal length.

Free

100 Questions 100 Marks 90 Mins

Given:

Rhombus ABCD , AB = 10 cm, so BC = 10 cm ( All sides of rhombus are equal)

Diagonal (AC) = 12 cm

Formula Used:

(1) Area of triangle = \(\sqrt {\left\{ {s\left( {s - a} \right)\left( {s - b} \right)\left( {s - c} \right)} \right\}} \)  Where s is to semi perimeter & a, b and c are sides of the triangle

(2) Area of rhombus (ABCD) = 2 × Area of Triangle 

Calculation:

⇒ Area of Δ ABC = \(\sqrt {\left\{ {s\left( {s - a} \right)\left( {s - b} \right)\left( {s - c} \right)} \right\}} \)

⇒ Semi perimeter of Δ ABC = (10 + 10 + 12)/2 

⇒ s = 16

⇒ Area of Δ ABC = \(\sqrt {\{ 16\left( {16 - 10} \right)\left( {16 - 10} \right)\left( {16 - 12} \right)} \} \)

⇒ \(\sqrt {16 × 6 × 6 × 4} \)

⇒ Area of Δ ABC = 4 × 2 × 6 = 48 \(c{m^2}\)

 Area of rhombus (ABCD) = 2 × Area of Triangle 

∴ Area of rhombus (ABCD) = 2× 48 = 96 \(c{m^2}\)

Stay updated with Quantitative Aptitude questions & answers with Testbook. Know more about Mensuration and ace the concept of Plane Figures and Rhombus

India’s #1 Learning Platform

Start Complete Exam Preparation

Daily Live MasterClasses

Practice Question Bank

Mock Tests & Quizzes

Get Started for Free Download App

Trusted by 3.4 Crore+ Students