# squared based on center point and area

Derek S. shared this question 8 years ago

How would you construct a square given its center point and area?

My first attempt:

• find the apothem:

apothem = sqrt(area) / 2

• create an apothem from center point A:

Segment[A, apothem]

• use the rotate tool three times to create the other apothems

• complete the square using lines parallel to the apothems

...other ideas? :-]

1

How would you construct a square given its center point and area?

My first attempt:

• find the apothem:

apothem = sqrt(area) / 2

• create an apothem from center point A:

Segment[A, apothem]

• use the rotate tool three times to create the other apothems

• complete the square using lines parallel to the apothems

...other ideas? :-]

A shorter version:

c=circle[A,sqrt(area) / 2]

Polygon[point[c,0],point[c,0.25],4]

Regards Abakus

1

That's an interesting approach. I wasn't aware of the Point[ <Object>, <Parameter> ] variation.

Although it needs a small tweak to produce a square with the original area,

because it is based on the length of half a diagonal, instead of an apothem.

c=circle[A,sqrt(area)*sqrt(2)/2]

Polygon[point[c,0],point[c,0.25],4]

and for the other orientation:

Polygon[point[c,0.125],point[c,0.375],4]

1

abakus method is fast and easy.

Here are two other approaches (area= A, center = C):

a) using Zip command and polar coordinates:

Polygon[Zip[C + (sqrt(A / 2); X), X, {0, π/2, π, 3π/2}]]

b) using complex numbers multiplication:

Polygon[Sequence[C + (sqrt(A / 2) + 0ί) ℯ^(ί π / 2 k), k, 0, 3]]

1

Thanks for the ideas. 8)