Semicircles
whose centers a
are the midpoints .
of the sides of
square abcd are .
drawn. if the
measure of each
side of the square
is 4 cm, what is the area, nearest to
the tenth of a sq cm, of the shaded
portion of the figure?

The area of the shaded portion of the figure is

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The shaded area is equal to the area of the square less the area not shaded.

There are 4 "not shaded" regions.

step 1

Find the area of square ABCD

The area of square is equal to

where

b is the length side of the square

we have

substitute

step 2

We can find the area of 2 "not shaded" regions by calculating the area of the square less two semi-circles (one circle):

The area of circle is equal to

The diameter of the circle is equal to the length side of the square

so

---> radius is half the diameter

substitute

Therefore, the area of 2 "not-shaded" regions is:

and the area of 4 "not-shaded" regions is:

step 3

Find the area of the shaded region

Remember that the area of the shaded region is the area of the square less 4 "not shaded" regions:

so

---> exact value

assume

substitute

333333333333333333333333333333

step-by-step explanation: