You haven't told us whether that 37 inches is the diameter
of the circle ... whether the line goes through the center of
the circle. If it doesn't , then we have no way to answer the
question without more information, so I guess I must assume
that it does.
The area of a whole circle is (pi) times (the radius squared).
The radius of a circle is 1/2 of the diameter.
For this circle, the radius is (37/2) = 18.5 inches,
and the (radius squared) is 342.25 inches² .
The area of the circle is (pi) (R²) = 1,075.210 inches²
The diameter divides the circle into two equal parts, and
one of them is shaded. So the area of the shaded part is ...
(1/2) x (1,075.210) = 537.61 inches²
Rounded to the nearest tenth: 537.6 inches²
