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

Video Solution

Solution Steps

00:06 Let's find the area of the rhombus.

00:10 The perimeter of a rhombus is the sum of all its sides.

00:16 Remember, in a rhombus, all sides are equal.

00:22 So, if all sides are equal, the perimeter is four times one side.

00:29 Let's substitute the perimeter value and find side D C.

00:36 This gives us the length of side D C in the rhombus.

00:46 In a rhombus, since all sides are equal, let's use the area formula.

00:58 The area formula is side times height.

01:08 Now, substitute the values and find the area.

01:18 And that's how we solve this 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