# Thread: Area of a Rhombus

1. ## Area of a Rhombus

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

2. Originally Posted by BrendanLoftus
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.

3. 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: . $x \:=\:\tfrac{1}{4}\text{(perimeter)}$

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

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

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

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