find the area of the shaded region in the figure assuming the quadrilateral inside the circle is a square.
x^2+y^2=36
(the picture is of a square inside a circle on a coordinate plane)
Apparently you have a circle of radius 6 inside a square of side 12
Do't know what was shaded, but just find the area of (part of?) the circle, and the area of (part of?) the square. Then subtract as needed
the shaded part isthe outside of the square. so how would i find that part?
sorry - misread the question. If the square is inside the circle of radius 6, then the diagonal of the square is a diameter of the circle.
That means the diagonal of the square is 12, and the sides are 6√2. The area of the square is thus 72.
So, now you know the area of the circle and the area of the square.
To find the area of the shaded region in the figure, we need to find the area of the circle and subtract the area of the square.
First, let's find the area of the circle. The equation x^2 + y^2 = 36 represents a circle with radius 6, since the general equation of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center of the circle and r is the radius. In this case, the center of the circle is the origin (0, 0), so the radius is 6.
The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius. Therefore, the area of the circle is A = π * 6^2 = 36π square units.
Next, let's find the area of the square. Since the quadrilateral inside the circle is assumed to be a square, we know that the circle's center is also the center of the square. The diagonal of the square is equal to the diameter of the circle, which is 2 * radius = 2 * 6 = 12.
The diagonal of a square divides it into two congruent right triangles. Each right triangle has a base and height equal to half the diagonal. So, the base and height of the right triangle (and thus the side length of the square) is 12 / 2 = 6.
Now, we can find the area of the square. The area of a square is given by the formula A = side length^2. Therefore, the area of the square is A = 6^2 = 36 square units.
Finally, we can find the area of the shaded region by subtracting the area of the square from the area of the circle: 36π - 36.
Therefore, the area of the shaded region is 36π - 36 square units.