# Area of a Rhombus

#### BrendanLoftus

What is the area of a rhombus when the only given information is it's perimeter?

#### pflo

What is the area of a rhombus when the only given information is it's perimeter?
There are four congruent sides to a rhombus, so each side is one-quarter of the perimeter. Divide the perimeter by 4 and you've got the length of each side.

The area is base*height, but you can't know what the height is without knowing how much of a slant the thing is at compared to a square.

Last edited:

#### Soroban

MHF Hall of Honor
Hello, BrendanLoftus!

What is the area of a rhombus when the only given information is its perimeter?

Since a rhombus is equilateral, each side is: .$$\displaystyle x \:=\:\tfrac{1}{4}\text{(perimeter)}$$

But the area can range from $$\displaystyle 0\text{ to }x^2.$$

Code:
                B
A o = = = = o = = = = o C
x    D    x

B o - - - - o C
/         /
/         / x
/         /
A o - - - - o D
x

B o - - - - o C
|         |
x |         |
|         |
|         |
A o - - - - o D
x

• pflo
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