It is 2*r^2.
6.5 units
Approximately 5.66x5.66 in. Or root32 x root32
The center of the rectangle to the corner of the rectangle is the radius of the circle. That can be found using the distance formula sqrt((5/2)^2+(12/2)^2) = 6.5 = r 5/2 is half the height of the rectangle and 12/2 is half the height of the rectangle. radius = 6.5
If you know the length of the side of the (regular) hexagon to be = a the radius r of the inscribed circle is: r = a sqrt(3)/2
radius
Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius a in C programming
The largest rectangle would be a square. If the circle has radius a, the diameter is 2a. This diameter would also be the diameter of a square of side length b. Using the Pythagorean theorem, b2 + b2 = (2a)2. 2b2 = 4a2 b2 = 2a2 b = √(2a2) or a√2 = the length of the sides of the square The area of a square of side length b is therefore (√(2a2))2 = 2a2 which is the largest area for a rectangle inscribed in a circle of radius a.
6.5 units
Approximately 5.66x5.66 in. Or root32 x root32
112cm2
The center of the rectangle to the corner of the rectangle is the radius of the circle. That can be found using the distance formula sqrt((5/2)^2+(12/2)^2) = 6.5 = r 5/2 is half the height of the rectangle and 12/2 is half the height of the rectangle. radius = 6.5
Assuming there is no border around the circle, then doubling the radius will give the length and width of a square (28 x 28 = 784cm2). The problem in your question is that you state it is a rectangle. Which means that the rectangle must be longer in length then width!
If you know the length of the side of the (regular) hexagon to be = a the radius r of the inscribed circle is: r = a sqrt(3)/2
2.8 cm
The radius of a circle inscribed in a regular hexagon equals the length of one side of the hexagon.
Yes.
radius