What Is a Square?
In the figure above, _BD_ is the diagonal of square _ABCD_.
| Quantity A | Quantity B |
|----|----|
| Half of the area of the shaded region | One-quarter of the area of square _ABCD_ |
Incorrect.
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The shaded region is bound by the diagonal of the square, which divides the square exactly in half. Taking half of the area of this region is not greater than a quarter of the entire area.
Incorrect.
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Dividing the area of the square into quarters can be accomplished by drawing two diagonals across the square. The area of one of these sections is not greater than half of the area of a shaded region bound by a single diagonal.
Correct.
The shaded region is exactly half of the area of the square. Dividing this area in half is the same as one-quarter of the area of the square.
Incorrect.
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There is enough information to solve the problem. In particular, note that the shaded region is bound by the diagonal of the square and therefore has exactly half of the area of the square.
Quantity A is greater.
Quantity B is greater.
The quantities are equal.
The relationship cannot be determined from the information given.
