Circumference of a parallelogram (diagnoals given only)

• ViresArcanum
In summary, the conversation discusses a parallelogram with diagonals of length 7 and 9 units and the question of finding its circumference. The equations for the diagonals are provided but the values for a and d are unknown. The conversation also discusses the conditions for a regular parallelogram where a=c and b=d, making alpha=gamma and beta=delta. However, without further information, the question cannot be answered definitively. A hint is given that the diagonals always intersect in the middle, but rotating them from the midpoint would change the circumference. Therefore, the question is not finite.
ViresArcanum

Homework Statement

Given is a parallelogram which has diagonals of the length 7 (e) and 9 units (f). How big is its circumference?

The sides are a,b,c,d; a being the bottom side, rest is anti-clockwise... alpha is the angle of a etc...

Homework Equations

no are given, i guess pythagoras or trig might be useful.

diagonals of a parallelogram (might be useful)

e=sqrt(a^2+d^2+2*a*d*cos(alpha))
f=sqrt (a^2+d^2-2*a*d*cos(alpha))

alpha=gamma
beta=delta
beta=180-alpha

The Attempt at a Solution

I tried using this first of all by drawing lots of triangles in the parallelogram and solve it with pythagoras or trig functions but without success

afterwards i tried using the formulas for the diagonals but without knowing a and d i didn't have much of a success either

is it a regular parallelogram, where a=d, b=c, or not regular one where all, a,b,c,d are of different value?
I am a little bit confused, are these
alpha=gamma
beta=delta
beta=180-alpha some other conditions that you are given, or what?

Last edited:
well, a=c and b=d

since the opposing sides are equally long, the opposing angles have to be equal as well; since a=c, alpha=gamma

these angle conditions are just normal rules for a regular parallelogram

hope, this is less confusing now...

I am giving a hint:

The diagonals of a parallelogram always intersect in the middle.

EDIT: Talking of midpoints, the question does not hold enough information. If you rotate any of the diagonals from the mid-point, the circumference (or is it the perimeter?) will vary. Thus the question is not finite.

Last edited:

1. What is the formula for finding the circumference of a parallelogram when only the diagonals are given?

The formula for finding the circumference of a parallelogram when only the diagonals are given is: C = 2(d1 + d2), where d1 and d2 are the lengths of the diagonals.

2. How is the circumference of a parallelogram related to its diagonals?

The circumference of a parallelogram is directly related to the lengths of its diagonals. In fact, the formula for finding the circumference involves adding the lengths of the diagonals together.

3. Can the circumference of a parallelogram be negative?

No, the circumference of a parallelogram cannot be negative. It is a measurement of distance, which is always a positive value.

4. How do I measure the diagonals of a parallelogram?

To measure the diagonals of a parallelogram, you can use a ruler or measuring tape. Place the measuring tool along one diagonal, starting at one corner, and extend it to the opposite corner. Take note of the measurement and repeat for the other diagonal. Make sure to record the lengths in the same unit of measurement.

5. Can I use the Pythagorean theorem to find the circumference of a parallelogram?

No, the Pythagorean theorem cannot be used to find the circumference of a parallelogram as it only applies to right triangles. The formula for finding the circumference of a parallelogram involves adding the lengths of the diagonals, not using the squares of their lengths.

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