It would be better if the writer had said 'diameter' not 'width' but that's what he meant.

You are right that the area of a circle is pi r^2 where r is the radius. In this example we know the diameter, not the radius. So let's get a new formula for the area using the diameter.

But the writer wants to use 'w' for the width of the square and the diameter of the circle so the formula becomes

Now you can compare this with the area w^2 of the square. Here percent means the percentage that the area of the circle is compared with the square.

Bob

]]>Square's Area = w^2 = 3^2 = 9 m^2

Estimate of Circle's Area = 80% of Square's Area = 80% of 9 = 7.2 m2

Circle's True Area = (Pi/4) × D2 = (Pi/4) × 32 = 7.07 m^22 (to 2 decimals)

The estimate of 7.2 m2 is not far off 7.07 m2

I found this in MIF link : https://www.mathsisfun.com/geometry/circle-area.html

it says area of a circle is = Pi/4 * r^2

but I used to use the formula only Pi * r^2

why the website multiply it by 1/4

I even didn't understand the headline : Comparing a Circle to a Square!!!

it said : A circle has about 80% of the area of a similar-width square.

how did he find that? maybe the circle is 70% of 50%

and how did he say : similar-width! it's first time I read about that term width of a circle