Problem
2002 AMC 8 Problem 20
The area of triangle XYZ is 8 square inches. Points A and B are midpoints of congruent segments \overline{XY} and \overline{XZ}. Altitude \overline{XC} bisects \overline{YZ}. The area (in square inches) of the shaded region is
![[asy]/* AMC8 2002 #20 Problem */ fill((0,0)--(2.5,2)--(5,2)--(5,0)--cycle, mediumgrey); draw((0,0)--(10,0)--(5,4)--cycle); draw((2.5,2)--(7.5,2)); draw((5,4)--(5,0)); label(scale(0.8)*"$X$", (5,4), N); label(scale(0.8)*"$Y$", (0,0), W); label(scale(0.8)*"$Z$", (10,0), E); label(scale(0.8)*"$A$", (2.5,2.2), W); label(scale(0.8)*"$B$", (7.5,2.2), E); label(scale(0.8)*"$C$", (5,0), S); fill((0,-.8)--(1,-.8)--(1,-.95)--cycle, white);[/asy]](/static/aops/e2bc37b5fd7b065251052d9936af8d9253a30b06.png)
\text{(A)}\ 1\frac{1}{2} \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 2\frac{1}{2} \qquad \text{(D)}\ 3 \qquad \text{(E)}\ 3\frac{1}{2}
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