Area of a circle with 1000m perimetre?

if perimter= circumference = 1000 = pi*d

then d = 1000/pi
r = 500/pi

so area = pi * r^2 = pi * 500/pi* 500/pi = 2500/pi m^2

(1000 / 2pi) = r (159.23)


pi * r^2 = area

25,354.192 * 3.14 = 79,612.165 sq m

The perimeter (also known as circumference) of a circle is

P = 2pi(r)

Since the perimeter is 1000,

1000 = 2pi(r), which means
r = 1000/(2pi), or
r = 500/pi

The area of a circle is

A = pi (r)^2

Plug r = 500/pi, to get

A = pi ( 500/pi )^2
A = pi ( 250000 / pi^2 )
A = 250000/pi

First, permit's relate area and Perimeter. The formulation for area is A = &pi r^2 The formulation for perimeter is P = 2 &pi r interior the 2nd formulation, permit's isolate r r = P/(2&pi) substitute this value into the 1st formulation. A = &pi r^2 A = &pi [P/(2&pi)]^2 A = &pi P^2 (a million/[4 &pi^2] ) Which extra simplifies as A = (a million/4) P^2 (&pi / &pi^2 ) And we get a cancellation A = (a million/4) P^2 (a million/&pi) And all of us understand P = 1000, so A = (a million/4)(1000)^2 (a million/&pi) A = ( a million/4 ) (a million/&pi) A = 250000/&pi

1000 = 2 π r
r = 1000 / (2 π)
A = π r ²
A = π 1000² / (4 π ²)
A = 1000² / (4 π)
A = 79,577 m²

You lazy idiot!!!

The equation for the perimeter, also known as the circumfrence, is:

Circumfrence = pi(diamter)

The equation for the area of a circle is:

Area = pi(radius^2)

In order to find the radius you must work backwards from the circumfrence that was given. So...

1000 = pi(diameter)
1000/pi = diameter

When you have the diameter, which should be about 318 m, you would divide it in half to get the radius and plug it into the area equation.

A = pi(159^2)
A = pi(25281)
A = 79382.34 meters squared

*I used 3.14 as pi, if you're working this out on a graphing calculator with the pi button then the results might be slightly off.

circumference=2pir
=(6.28)r
1000 m/6.28=r
159.24 m=r

Area=pir^2
Area=(3.14)(159.24)^2
Area=(3.14)(25,357.38)
Area=79,622.17 m^2

3.14(1000/3.14/2)^2
= 3.14(500/3.14)^2
= 3.14(159)^2
= 3.14(25281)
= 79382.34 meter squared

This is the quickest method.
Perimeter of circle = 2 * pi * radius = 1000
=> pi* radius = 500
squaring both sides,
pi^2 * radius^2 = 500^2
pi* radius^2 = (500^2)/pi
Now , area of circle = pi * radius^2
= (500^2)/pi (from above)
= 79577.47 m^2