Question

Find the area of the shaded region. Use 3.14 for π.

Answer 1

The aswer to this question is really quite easy.

Since we know that the shaded area is a square, finding its area is a simple matter. Its area is s^2, or s squared, where s is the length of one edge of the square.

To find the area of the circle, we use the fact that for any circle, its area is A = pi x r^2, or pi times r squared, where r is the radius of the circle. To find a circle's radius, measure from the circle's center to any point on the circumference of the circle. Multiply r by itself. Then multiply that result by pi. That gets you the area of the circle.

What you seem to be looking for is the shaded area of the square remaining after removing the area of the circle. To do this, simply subtract the area of the circle from the area of the square.

Your formula should look something like this:

A (shaded) = A (square) - A (circle)
= s^2 - (pi x r^2)

Notice that it does contain the constant pi.

If your circle is tangent to all sides of the square in which it is inscribed (a single point on the circumference of the circle touches each side of the square at its mid-point), then your job is made easier still.

A circle tangent to a circumsribed square (in this case a square constructed outside of the circle) has a radius equal to half the length of a side of the square.

Then the above formula collapses to:

A (shaded) = s^2 - (pi x (s/2)^2)
= s^2 - (pi x (s^2/4))

Note s^2/4 is read s squared divided by four.

Factoring out common factors, we get

A (shaded) = s^2 x (1) - s^2 (pi/4)
= s^2 x (1 - pi/4)

Note that pi/4 is less than 1, so (1 - pi/4) is a positive number.

Answer 2

https://answers.yahoo.com/question/index?qid=20061105154832AAr4xAR

Answer 3

thanks;)