Calculate Rhombus Area: Given Perimeter P=50 and Diagonal Length 8

Video Solution

Solution Steps

00:00 Find the area of the rhombus

00:04 The perimeter of the rhombus equals the sum of its sides

00:10 In a rhombus all sides are equal

00:16 If all sides are equal, then the perimeter equals 4 times one side

00:23 Let's substitute the perimeter value and solve for DC

00:30 This is the side length (DC) in the rhombus

00:40 In a rhombus all sides are equal

00:52 Let's use the formula for rhombus area (side times height):

01:02 Let's substitute the appropriate values and solve for the area

01:12 And this is the solution to the problem

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