Rhombus area - Examples, Exercises and Solutions

How is the area of a rhombus calculated?

Every geometric problem is based on a wealth of data, whose answer is divided into several different questions. One of the most popular questions, and the one most likely to appear on your test, is the question about the area of a rhombus. As is well known, a rhombus consists of 2 2 different triangles. If so, how do you calculate its area?

Rhombus Formula

Area=Diagonal1×Diagonal22 Area=\frac{Diagonal_1\times Diagonal_2}{2}

  • The formula to calculate the area of a rhombus: Diagonal × \times Diagonal, divided by 2 2 .
  • Another formula you can think of for the area of a rhombus (depending on the information provided by the question): Base × \times Height.

Practice Rhombus area

Exercise #1

Given the rhombus in the drawing:

444777

What is the area?

Video Solution

Step-by-Step Solution

Let's remember that there are two ways to calculate the area of a rhombus:

The first is the side times the height of the side.

The second is diagonal times diagonal divided by 2.

Since we are given both diagonals, we calculate it the second way:

7×42=282=14 \frac{7\times4}{2}=\frac{28}{2}=14

Answer

14

Exercise #2

Look at the rhombus in the figure.

What is its area?

P=50P=50P=50888

Video Solution

Step-by-Step Solution

First, let's remember that according to the properties of a rhombus, all sides of a rhombus are equal,

Therefore, if we define the sides of the rhombus with the letters ABCD,

We can argue that:

AB=BC=CD=DA

We use the perimeter formula:

50 = AB+BC+CD+DA

And we can conclude that
 4AB=50

(We can also use any other side, it doesn't matter in this case because they are all equal.)

 

We divide by four and reveal that:

AB=BC=CD=DA = 12.5

 

Now let's remember the formula for the area of a rhombus: the height times the side corresponding to the height.

We are given the length of the external height 8,

Now, we can replace in the formula:

8*12.5=100

Answer

100 cm²

Exercise #3

Given the rhombus in the drawing:

555333

What is the area?

Video Solution

Step-by-Step Solution

Remember there are two options to calculate the area of a rhombus:

Diagonal by diagonal divided by 2.

Side by the height of the side.

In the question, we are only given half of the diagonal and the side, which means we cannot use any of the formulas.

We need to find more data. Let's find the second diagonal:

Remember that the diagonals of a rhombus are perpendicular to each other, which means they form a 90-degree angle.

Therefore, all the triangles in a rhombus are right-angled.

Now we can focus on the triangle where the side and the height are given, and we will calculate the third side by the Pythagorean theorem:

a2+b2=c2 a²+b²=c² Replace the data:

32+x2=52 3^2+x^2=5^2 9+x2=25 9+x^2=25 x2=259=16 x^2=25-9=16 x=16=4 x=\sqrt{16}=4 Now that we have found half of the second diagonal, we can calculate the area by diagonal by diagonal:

Since the diagonals in a rhombus are perpendicular and cross each other, they are equal. Therefore our diagonals are equal:

3+3=6 3+3=6 4+4=8 4+4=8 Therefore, the area of the rhombus is:

6×82=482=24 \frac{6\times8}{2}=\frac{48}{2}=24

Answer

24

Exercise #4

Calculate the area of the rhombus in the figure below:

555222

Video Solution

Answer

10 cm²

Exercise #5

In the drawing given a rhombus

The length of each side of the rhombus is 5 cm

The length of the height of the side is 3 cm

What is the area of the rhombus?

555555555555333

Video Solution

Answer

15 cm².

Exercise #1

Look at the rhombus in the diagram below.

What is the area of the rhombus?

555333

Video Solution

Answer

7.5 cm²

Exercise #2

Given the rhombus in the figure

What is your area?

999999999999444

Video Solution

Answer

36 cm².

Exercise #3

Given the rhombus in the figure

What is your area?

101010888

Answer

80 cm²

Exercise #4

In the drawing given a rhombus

The length of the main diagonal 6 cm

The length of the secondary diagonal 4 cm

What is the area of the rhombus?

666444

Video Solution

Answer

12 cm²

Exercise #5

Look at the rhombus in the figure.

What is its area?

777666

Video Solution

Answer

42 cm²

Exercise #1

A rhombus and its external height are shown in the figure below.

The length of each side of the rhombus is 5 cm.

What is its area?

333

Video Solution

Answer

15 cm².

Exercise #2

Given the rhombus whose length of its sides is 8 cm

The length of the given height is 5 cm

What is the area of the rhombus?

888555

Video Solution

Answer

40 cm²

Exercise #3

Given the rhombus in the drawing:

888131313

What is the area?

Video Solution

Answer

52

Exercise #4

The rhombus in the diagram has an area of 24 cm².

XXX888

What is the value of X?

Video Solution

Answer

6

Exercise #5

Given the rhombus in the drawing:

666111111

What is the area?

Video Solution

Answer

33

Topics learned in later sections

  1. Area
  2. Rhombus, kite, or diamond?