Find the area of the shaded portion in the square. show all work for full credit.
(hint: assume the central point of the arc is the corresponding corner.)

Step-by-step explanation:

In order to find the area of the shaded area you first need to find the area of the circle segment. The easiest way to do this would be to use the equation: you would substitute r with the radius which in this case is 6:

This would give you the answer

Because the picture only shows you 1/4 of the circle, you will need to divide by 4. This gives you .

Now, in order to find the area of the shaded area you will need to subtract by the area of the square. The square has side lengths of 6, and in order to find the area, you will multiply 6 by 6 to get 36.

Now you will subtract to get:

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet