A square is inscribed in a circle with a diameter of 4 cm. What is the perimeter of the square?

Question

A square is inscribed in a circle with a diameter of 4 cm. What is the perimeter of the square?

Answer 1

In an inscribed square, the diagonal of the square is the diameter of the circle(4 cm) as shown in the attached image.

So by pythagorean theorem (or a 45-45-90) triangle, we know that a side is 2√2). The full calculation is shown below:

a² + b² = c²
In a square, the two legs (sides) are equal, so
a = b
c = 4
a² + a² = 4²
2a² = 16
a² = 8
a = √8 = √4√2 = 2√2

The perimeter of the square is 4 times this or 8√2. Calculating this out, the approximate perimeter is: 11.3 cm.

Answer 2

When the square is inscribed in the circle with diameter 4cm, the diagonal of the square is the same as the diameter. (I can't illustrate it here, but draw a picture, and you'll see what I mean)

The diagonal of a square forms two triangles each with 45-45-90 degree angles. A 45-45-90 degree triangle is known to have sides in proportion of 1-1-sqrt(2). 1 and 1 are the legs and sqrt(2) is the hypotenuse. Since the diagonal here is also the hypotenuse of both triangles, (1 / sqrt(2) ) = (leg length / 4).

Leg length = 4 / sqrt(2) = 2*sqrt(2). There are 4 legs, all making up the sides of the square.

Perimeter of square = 4 * length of side = 4 * 2sqrt(2)
=8sqrt(2) cm

Answer 3

Because a square has all sides of equal length, the diameter of the circle is actually the diagonal of the square. Thus, you can find the length of one side of the square s using the Pythagorean Theorem:

s^2 + s^2 = 4^2
2*s^2 = 16
s^2 = 8
s = sqrt(8) = 2 * sqrt(2)

Since a square has four sides, just multiply this by four to find the perimeter:

2 * sqrt(2) * 4 = 8 * sqrt(2) ~= 11.3 cm^2

Answer 4

The hypotenuse of the inscribed square will be the diameter of the circle. If its side is equal to a, then 2a*a = 16 and a = 2√2 = 2.82. The perimeter is four times the side and is equal to 11.28 cm.

Answer 5

8squareroot of 2!

the diameter of the circle is the diagonal of the square, the angle between the 2 diagonal of the square is 90 degrees therefore you have two congruent triangles, 45 by 45 by 90 degrees 2 is the height of the triangle and 4 is the base, draw it!
bh/2
2*4/2=area of the triangle=4
there are two of them=so 4 times 2= 8
8= area of the square
square root of 8= 2squarerootof2=side

there are 4 equal sides in a square so 4 times the side, since side=2squarerootof2, 4 times 2 square root of 2 is 8squareroot of 2!

Answer 6

The diagonals of the square are diameters of the circle and therefore have length 4 cm.

Because the diagonal = V2 times the side, the side has length a = 4/V2 = 2V2.

Four sides together make a perimeter of
8V2 = 11.314 cm

Answer 7

heres how you do it
the diagonal of the square has to be 4, cause thats the perimeter, so by the pythagorean theorem, a^2+b^2=16
since you are working with a square a and b are equal, so 2a^2=16
a^2=8
a=Sqrt(8)
and the perimeter is 4Sqrt(8)

Answer 8

The square's diagonal forms the diameter of the circle

a^2 + b^2 = c^2

a = b

a^2 + a^2 = 4^2
2a^2 = 16
a^2 = 8
a = 2sqrt(2)

P = 4a
P = 4(2sqrt(2))
P = 8sqrt(2)

ANS : about 11.314cm

Answer 9

4*sqroot(8) because the diameter is also the hypotinues of the triange made bissecting the square from opposite corners, therefore using a2+b2=c2 (a and b are the same) gives u 4*sqroot(8)

Answer 10

8*(2)^(1/2)