Question 1181243
<br>
Look at the diagram with AC a side of the rhombus and the semicircle with center B on side AC and radius BD.<br>
{{{drawing(400,400,-1,5,-1,5,
line(0,0,3,0),line(3,0,4.5,1.5*sqrt(3)),line(0,0,1.5,1.5*sqrt(3)),line(1.5,1.5*sqrt(3),4.5,1.5*sqrt(3)),graph(400,400,-1,5,-1,5,sqrt((1.3923^2-(x-1.6077)^2))),
line(1.6077,0,0.4019,0.696),
locate(-0.3,-0.1,A),locate(1.6,-0.1,B),locate(3.2,-0.1,C),locate(0.2,0.9,D)
)}}}<br>
Let r be the radius of the semicircle, BD; BC is also a radius.<br>
Triangle ABD is a 30-60-90 right triangle in which the radius is the long leg.  That makes the length of AB {{{(2/sqrt(3))r}}}.<br>
But AB+BC=BC=3.  So<br>
{{{(r)+((2/sqrt(3))r)=3}}}<br>
Use a calculator to solve that to find the radius; then use the formula for the area of a semicircle to get the answer to the problem.<br>
I leave that much of the problem to you.<br>
Note my result for the area of the semicircle is 3.045 square units, which is actually good to 4 decimal places.<br>