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 =

if x = 1, then the answer is 3.5

answer 1 : option "c"

answer 2 : option "d"

answer 3 : option "b"

answer 4 : option "d"

answer 5 : option "b"

answer 6 : option "a"

answer 7 : option "c"

answer 8 : option "d"

answer 9 : option "c"

answer 10 : option "d"

answer 11 : option "c"

answer 12 option "b"

answer 13 option "c"

answer 14 option "c"

answer 15 option "d"

answer 16 option "a"

answer 17 option "b"

answer 18 option "c"

answer 19 option "a"

answer 20 option "a"

answer 21 option "c"

d