beginning of content:
SAT Subject Test
Rectangle is inscribed in the circle shown above. If the length of side
is
and the length of side
is
, what is the area of the shaded region?
Select an Answer
Correct Answer:
No
Correct Answer:
No
Correct Answer:
Yes
Correct Answer:
No
Correct Answer:
No
View Correct Answer
The correct answer is C.
The area of the shaded region can be found by subtracting the area of rectangle from the area of the circle. To determine the area of the circle, first find the radius
, and then compute the area
. Since rectangle
is inscribed in the circle,
is an inscribed right angle, and thus
is a diameter of the circle. Applying the Pythagorean theorem to right triangle
,one finds the length of side
is
Thus the radius of the circle is
, and the area of the circle is
. The area of rectangle
is
, and therefore, the area of the shaded region is
.
Question Difficulty:
hard