A square is inscribed in the circle x^2+y^2=32. Find the area of the square.
- la consoleLv 71 month agoFavorite Answer
x² + y² = 32
(x - 0)² + (y - 0)² = (√32)²
The typical equation of a circle is: (x - xo)² + (y - yo)² = R² → where:
xo: abscissa of center → 0 in your case
yo: ordinate of center → 0 in your case
R: radius of circle → √32 in your case → then the diameter is: d = 2√32
As the square is inscribed in the circle, the diameter of the circle is the diagonal of the square.
The surface area of the square is:
a = s² ← where s is one of the sides of the square
According the Pythagorean's theorem, you can see that:
s² + s² = d² ← where d is the diagonal of the square, i.e. the diameter of the circle
2s² = d²
s² = d²/2 → recall: a = s²
a = d²/2 → recall: d = 2√32
a = (2√32)²/2
a = (4 * 32)/2
a = 64
- DavidLv 71 month ago
Circle equation: x^2 + y^2 = 32
Circle center: (0, 0)
Radius of circle: square root of 32 = 4 times square root of 2
Diameter of circle: 8 times square root of 2
Sides of square using Pythagoras: 8
Area of inscribed square: 8 times 8 = 64 square units
- Φ² = Φ+1Lv 71 month ago
The area of a square is the half the square of the diagonal.
The area of a square is the half the square of the diameter of the circumscribed circle.
The area of a square is the double the square of the radius of the circumscribed circle.
The square of the radius of the circle is 32, so the area of a square is 64 square units.
- KrishnamurthyLv 71 month ago
Since the square is inscribed in the circle,
the diagonal distance between opposite corners is √32.
x^2 + y^2 = √(32)^2, where 'c' is the diagonal (which is √32) across the square,
and forms the hypotenuse of a right triangle.
Since this is a square, we know that x = y.
So we know that x^2 + x^2 = (16)^2.
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- Geeganage WLv 51 month ago
Let the apex of the square on the circle be (x, y) in the first quadrant. But x=y for a square.
Area, A = 4yx=4x^2.
x^2 + (x)^2 = 32.
A = 64.
Or, you may use the diagonal length = diameter of the circle = 2√32 =8√2.
Area = 8√2*8√2/2 = 64.
- TomVLv 71 month ago
The diagonal of the square is the diameter of the circle = 2√32 = 8√2
The square of the diagonal is twice the square of the side of the square:(8√2)² = 2s²
s² = 2(8)²
s² = 64
Area of the square is the square of the side of the square:
A = s² = 64
- Anonymous1 month ago