The circumference of a circle is 6.82. what is the area of the circle?

A= C^2/ 4π

A= 6.82^2/ 4π

A= 46.5124/ 4π

A= 3.70133918753

A≈ 4

The area of the circle is about 4

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4