What is the area, in square centimeters, of a circle that has a circumference of 16 centimeters?

Step-by-step explanation:

We know that the circumference of a circle is given by :-

, where r is the radius of the circle .

Given : Circumference of circle = 16 cm

Then,

i.e          (1)

We know that the area of circle is given by :-

i.e.                    [From (1)]

i.e.

i.e.

Put

Hence, area of circle =

look at the picture.

1.

ef : ab = 2 : 3

gf : cb = 2 : 3

gh : cd = 2 : 3

he : da = 2 : 3

2.

∠a ≅ ∠e

∠b ≅ ∠f

∠c ≅ ∠g

∠d ≅ ∠h

3.

use pythagorean theorem:

the length of the abcd trapezoid sides:

|ab| = 3 cm

|bc| = 10 cm

|cd| = 3(3) cm = 9 cm

|da| = 8 cm

the perimeter of abcd = 3 + 10 + 9 + 8 = 30 cm

the ratio of perimeters of the tarapezoids is equal 2 : 3.

substitute:

      cross multiply

      divide both sides by 3