i need to find the area of a square?

Question

Suppose you inscribe a square in a circle of radius . Thus all four corners of the square lie on the circle. The area of that square is??

Answer 1

The diagonal of the square is 2r, the side of the square is 2r/(sqrt 2) = sqrt 2 * r
The area is 2*r*r

Answer 2

ok, let's call the square ABCD. Points A, B, C, and D lie on the circle. We know the radius of the circle (let's say it's x). Diagonals of the square, then (AC) would be of length 2x (2 times the radius). Now you have a right triangle (ABC) with a right angle at B (remember, it's a square?) and two equal legs (squares have equal sides). Now use the pythagorean theorem to calculate the length of each side. Square the length of each side and you have the area of the square.

Answer 3

If the radius of the circle is r, then the diagonal of the square is 2r. So a side of the square would be 2r/√2.

The area of the square is (r√2)² = 2r².

Looks like m_if_you_please got it already.

Answer 4

The length of the circle's diameter (two times the radius) is the length of one side of the square. Then square that side (BasexHeight).

Answer 5

Jackii is wrong sorry,

the diameter of the circle is the same as the diagonal of the square.

seeing that the diagonal is also the hypotenuse of the triangle making up half the square, use pythagoras theorem to work out one of the sides of the square.

let x = side of square
let y = side of hypotenuse

y^2= 2x^2

after finding out the x, square it to get the area

Answer 6

2 x r x r where r is the radius of the circle

Answer 7

Length times Width