A square with the area of 81 meters squared is inscribed in a circle. What is the area of the circle?

Answer 1

OK, your square has an area of 81, so the sides would be 9.

The diameter of the circle would be sqr(9^2+9^2) orsqr(2*9^2) or
sqr(162) or 12.727922061357855439215198517887.

The raidus would be 1/2 of that, or 6.3639610306789277196075992589436.

The area of the circle would pi(6.36396103067892771960759925894360)^2 or pi*40.5 or 127.23450247038662615773705702282 square meters.

Answer 2

Draw a picture to help figure it out.

Since a square has all equal sides, each side is the square root of 81, or 9. Unfortunately, this doesn't help a lot with the circle. However, the diagonal of the square (traced from one corner to the opposite corner) will be diameter of the circle. The length of this diagonal can be calculated using the Pythagorean Theorem.

a squared + b squared = c squared
81 + 81 = 162. Square root of 162 is about 12.73.

Area = pi * radius squared. Since the diameter is 12.73, the radius is about 6.37.
So Area = 127.27 meters squared.

If you need an exact answer, you'll have to keep the square roots and pi.

so pi * (square root of 162 divided by 2)squared = 40.5pi

Answer 3

okay this is how it goes....

because the square is 81...it had to be 9x9. you also know that a diagonal of the square is the diameter of the circle...so you divide the square into 2 triangles using 1 diagonal. you know that its a right triangle, with 2 sides of 9 and one side of X. you use the pythagorean thyrem next... so you get 9^2+9^2=X^2
that gives you 162=X^2...take the square root of both sides to get 9(sqrt(2)). Then..because you need the radius of the circle not the diameter which you just found, you divide it by 2. so you get

(9(sqrt(2)))/2. The area of the circle is (pie)(radius^2)....so plug it in and you got ur answer.

hope i helped

Answer 4

Area of square = 81 = length x width
Since it's a square, length = width
Area of square = 81 = length^2
Length = sqrt 81
We want to find the diagonal in the square (the hypotenuse of a right triangle).
a^2+b^2 = c^2
(sqrt81)^2+(sqrt81)^2 = c^2
162 = c^2
so, c = sqrt 162.
Now we know the diameter of the circle, so divide it by two to get the radius, and plug it into the circle area equation, (pie)r^2
(pie)(sqrt162/2)^2 = area of circl
(pie)(162/4) = area
In a calculator, this comes to 127.17 meters squared

Answer 5

First figure the diagonal of the square (which is the diameter of the circle). Each side of the sqaure is 9 meters (area : 9x9=81)

The diameter of the circle is the square root of 9^2 + 9^2 (12.73)
remember Pythagorean theorem (a^2 + b^2 = c^2)

Area of circle is pi * r^2
12.73/2 = 6.365
6.365 * 6.365 * 3.14 = 127.21 sq. meters

Answer 6

a million. The degree of an perspective is 360 divided by employing the facets of the polygon. 360/12 = 30 levels 2. The apothem is sq. root(3) 3. The apothem ia onw a million/2 of the sq.'s area length or 8 4. the size element is a million/4 5. (4/9) = pi*r^2/pi*r^2 = (r/3)^2 x = 2 6. The apothem's length is 6

Answer 7

A = s^2
81 = s^2
s = 9

a^2 + a^2 = d
2a^2 = d
2(9^2) = d^2
d^2 = 162
d = 9sqrt(2)

A = (9sqrt(2)/2)^2 * pi
A = (81pi/2) or about 127.2345 meters

If you are talking about the circle without the square inside, then the answer is 40.5pi meters, but if you are talking about the area of the circle with the square, then

40.5pi - 81 = about 46.2345 meters

Answer 8

Area of square=81m^2
side of square=9 m
Diagonal of squre=9*sqrt2
=diameter of circle
Area of circle
=Pi*dia^2/4
=[22/7]*[9sqrt2]^2/4
=127.17 m^2

Answer 9

diameter ofthe circle=diagonal of thesquare
=80rt2/4=40rt2 m
area=pir^2
=3200pi sq.metres.