Acircle is cut from a square piece of cloth, as shown: a square, one side labeled as 34 inches, has a circle inside it. the circle touches all the sides of the square. the portion of the square outside the circle is shaded. how many square inches of cloth are cut from the square? (π = 3.14) 907.46 in2 986.32 in2 1,024.00 in2 1,156.00 in2

You can use the fact that the cloth piece cut is circular and its area will give the area of cloth piece that is cut from the square piece of cloth.

The area of the cloth piece cut from the square is:

Option A: 907.46 square inches

Since the circle is fully fitted, its longest chord which is diameter must be touching both the bottom side and top side, and both the left and right side.  The opposite side of squares will serve as two tangents on the opposite ends of diameters of that circle. Thus, being perpendicular to other two pair of sides, we have the length of the diameter of the circle which is inside the square  is equal to the length of side of square.

Since the diameter of the circular cut piece is of the same length as that of the side of the square,thus, we have:

diameter of circle = 34 inches.

Thus, radius of circle = diameter/2 = 17 inches.

Thus, area of that circular cloth piece is obtained by:

Thus,

The area of the cloth piece cut from the square is:

Option A: 907.46 square inches

Learn more about radius and area of circle here:

link

both equations and proportions are better.

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.