### A circle of radius 28cm is opened to form a square. What is the maximum...

A circle of radius 28cm is opened to form a square. What is the maximum possible area of the chord?

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Sorry, i think there is a mistake in this question because A chord of a circle is a straight line segment whose endpoints both lie on the circle.
MY point is, a chord is simply a straight line, It doesnt have an area. In that case, i'll have to assume that you mean't.

A circle of radius 28cm is opened to form a square. What is the maximum possible area of the Square.

see below.

First of all, you can't really use a circle to build a square, unless you first of all draw the square in the circle, then cut it.

With that imagination now, let us soolve this question.

NB. All sides of the square are equal.
The diameter is D=2r
D=28x2=56cm

The principle to solving this question is that for the square to be at maximum fit, the diagonal must be equal to the diameter of circle.

from the diagonal we can find the Other sides of the square, using pythagoras theorem +.

see image below to get full understanding.
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The area of the original sheet = (pi)r^2 = (22/7)*196 = 616 sq cm.

The area of the 2 small circles cut out = 2*(pi)r^2 = 2(22/7)*3.5^2 = 77 sq cm.

The area of the remaining sheet = 616–77 = 539 sq cm.
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The area of the original sheet = (pi)r^2 = (22/7)*196 = 616 sq cm.

The area of the 2 small circles cut out = 2*(pi)r^2 = 2(22/7)*3.5^2 = 77 sq cm.

The area of the remaining sheet = 616–77 = 539 sq cm.
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pi*r^2
where pi=22/7
r=28cm
from the equation
pi*r^2 = 22/7*28/2*28/2
NOTE: IF IT IS TO FIND THE RADIUS THEN it will be 22/7*28*28 but for chord it will be
pi*r^2 = 22/7*28/2*28/2
=22/7*14*14
=22/7*196
=22*28
=616cm
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