Question 655352
if you look closely at shaded area, you will see that that area could be calculated as following:

you have a square inside ellipse with sides  {{{12.5cm}}} and {{{8.4cm}}}, so its
area is: 

{{{Area_square =12.5cm*8.4cm}}}

{{{Area_square =105cm^2}}}

than you have two half circles with same diameter of {{{8.4cm}}} that you should deduct from the area of the square, and these two halves make one full circle with area {{{C=r^2pi}}} where {{{r=8.4cm/2=4.2cm}}}

so, we have

{{{Area_circle1 = r1^2pi}}}

{{{Area_circle1 = (4.2cm)^2*3.14}}}

{{{Area_circle1 = 55.3896^2cm^2}}}

find their difference:

{{{Area_square -Area_circle1=105cm^2-55.3896^2cm^2}}}

{{{Area_square -Area_circle1=49.6104cm^2}}}

finaly, you have two half circles, one on left and one on right side of the square, that make one full circle...its diameter is {{{12.5cm}}}; so, its radius is {{{r2=6.25cm}}} and the area will be

{{{Area_circle2 = r2^2pi}}}

{{{Area_circle2 = (6.25cm)^2pi}}}

{{{Area_circle2 =122.65625cm^2}}}


now, your shaded area will be:{{{(Area_square -Area_circle1) +Area_circle2}}} 

{{{(Area_square -Area_circle1) +Area_circle2=49.6104cm^2+122.65625cm^2}}} 

{{{(Area_square -Area_circle1) +Area_circle2=172.26665cm^2}}} ...round to one decimal place


{{{(Area_square -Area_circle1) +Area_circle2=172.3cm^2}}}


so, your answer is {{{172.3cm^2}}}