# what is the area of the largest quadrileteral that can be inscribed in a circle with an area of 64pie? 1. 64 2. 72 3. 96 4. 108 5. 128

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baxthum8 | Certified Educator

The largest quadrilateral that can be inscribed in a circle is the square whose diagonal is the diameter of the circle.

Since the circle's area is: `A = 64pi,`

This means that `64 = r^2,`

so the radius of the circle is `8.`

Now, that makes the length of the diagonal of the square equivalent to: `16.`

The diagonal is the hypotenuse length of a `45-45-90 triangle.`

When given the hypotenuse of this special triangle the length of the sides are: `16 /sqrt(2)`

Simplified this gives the square a side length of `8sqrt(2).`

Since this isa square and all side lengths are equal to find area of square: `A = s^2.`

So `A = (8sqrt(2))^2`

**So the area of the square (the largest) is** `128.`