Examples with solutions for Area of a Rhombus: Finding Area based off Perimeter and Vice Versa

Exercise #1

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 #2

Given the rhombus in the figure

What is your area?

P=24P=24P=24555

Video Solution

Answer

30 cm²

Exercise #3

Look at the rhombus in the figure.

Calculate its area in terms of X.

P=20XP=20XP=20XX+3X+3X+3

Video Solution

Answer

5x2+15x 5x^2+15x

Exercise #4

Look at the rhombus in the figure.

P=4X+20 P=4X+20

The area of the rhombus can be represented by the expression:11X+55 11X+55

Work out the height of the side.

S=11X+55S=11X+55S=11X+55

Video Solution

Answer

11 11 cm