If the folded napkin spans the plate and the plate has an 18-inch diameter, what is the area of the space on the plate that is NOT covered by the napkin

Area not covered by napkin = 92.47 sq. in.

Step-by-step explanation:

Complete Question:

A square napkin is folded in half on the diagonal and placed on the diameter of a round plate . If the folded napkin spans the plate and the plate has an 18-inch diameter, what is the area of  the space on the plate that is NOT covered by the napkin?

Solution:

NOT covered area is basically:

Area of Circular Plate - Area of Square Napkin

Area of Circle is given by the formula:

Where r is radius, half of diameter (diameter is 18, so radius is 9)

Area of Square =

Where s is side length

Diagonal is given as same as diameter, which is 18. We can use pythagorean theorem to find side length of square:

Now, finding the areas:

Area of circle =

Area of Square =

Area of NOT COVERED AREA =

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step-by-step explanation: