Good at math? Help me with this?

Question

A square is inscibed in a circle with a three-inch diameter. What is the area of the square? please explain your reasoning :)

Answer 1

Draw a circle. Now draw a square inside the circle.

Draw a line from the center of the circle to a corner of the square. This line is a radius.

Now draw a line to create a triangle that
1) is a right triangle and
2) has a hypotenuse of the radius that you just drew

Now label the last line you drew as x.

Using pythagorean theorem
x^2 + x^2 = (3/2)^2 .......... (x^2 is x squared)

Thus
2x^2 = 9/4
x^2 = 9/8
x = Sqrt(9/8)

The area of the square is (2x)^2 so that will be 4x^2, which is 9/2 inches^2 = 4.5 in^2

Answer 2

Diameter of the circle = Diagonal of the square = d = 3 inches
Area of the square = (d^2)/2 = 3^ 2/2 =9/2 =4.5 square inches.

Answer 3

As square is inscribed in the circle , so diagonal of square become the diameter of circle...diagonal= 3
now side of square= diagpnal/ square root(2)
so , side of square= 3// square root(2)

Area of square= side^2=(3// square root(2))^2= 9/2=4.5

Answer 4

you have the diagonal d. Then the square is the sum or four right triangles of area each 1/2 x d/2 x d/2. Just conclude.

Answer 5

Each line drawn from the centre of the circle to each vertex of the square is a radius.
This should help you formulate a strategy to solve this problem.

Answer 6

diameter of circle=diagonal of square(d)=3inch
d=square root of sides(A) of square
3=squareroot(a^2+a^2)
squaring on both sides
9=2a^2
a^2=4.5
(a^2=area of square)
All the best

Answer 7

diameter = diagonal = 3 in
l² = diagonal²/2
L² = 3²/2
L² = 9/2
L = \/4.5 in