Difference between revisions of "2002 AMC 8 Problems/Problem 20"
Mrdavid445 (talk | contribs) (Created page with "The area of triangle <math>XYZ</math> is 8 square inches. Points <math>A</math> and <math>B</math> are midpoints of congruent segments <math> \overline{XY} </math> and <math> \ov...") |
Mrdavid445 (talk | contribs) |
||
Line 1: | Line 1: | ||
The area of triangle <math>XYZ</math> is 8 square inches. Points <math>A</math> and <math>B</math> are midpoints of congruent segments <math> \overline{XY} </math> and <math> \overline{XZ} </math>. Altitude <math> \overline{XC} </math> bisects <math> \overline{YZ} </math>. What is the area (in square inches) of the shaded region? | The area of triangle <math>XYZ</math> is 8 square inches. Points <math>A</math> and <math>B</math> are midpoints of congruent segments <math> \overline{XY} </math> and <math> \overline{XZ} </math>. Altitude <math> \overline{XC} </math> bisects <math> \overline{YZ} </math>. What is the area (in square inches) of the shaded region? | ||
− | + | <asy> | |
/* AMC8 2002 #20 Problem */ | /* AMC8 2002 #20 Problem */ | ||
draw((0,0)--(10,0)--(5,4)--cycle); | draw((0,0)--(10,0)--(5,4)--cycle); | ||
Line 7: | Line 7: | ||
draw((5,4)--(5,0)); | draw((5,4)--(5,0)); | ||
fill((0,0)--(2.5,2)--(5,2)--(5,0)--cycle, mediumgrey); | fill((0,0)--(2.5,2)--(5,2)--(5,0)--cycle, mediumgrey); | ||
− | label(scale(0.8)*" | + | label(scale(0.8)*"$X$", (5,4), N); |
− | label(scale(0.8)*" | + | label(scale(0.8)*"$Y$", (0,0), W); |
− | label(scale(0.8)*" | + | label(scale(0.8)*"$Z$", (10,0), E); |
− | label(scale(0.8)*" | + | label(scale(0.8)*"$A$", (2.5,2.2), W); |
− | label(scale(0.8)*" | + | label(scale(0.8)*"$B$", (7.5,2.2), E); |
− | label(scale(0.8)*" | + | label(scale(0.8)*"$C$", (5,0), S); |
− | fill((0,-.8)--(1,-.8)--(1,-.95)--cycle, white); | + | fill((0,-.8)--(1,-.8)--(1,-.95)--cycle, white);</asy> |
<math> \textbf{(A)}\ 1\frac{1}2\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 2\frac{1}2\qquad\textbf{(D)}\ 3\qquad\textbf{(E)}\ 3\frac{1}2 </math> | <math> \textbf{(A)}\ 1\frac{1}2\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 2\frac{1}2\qquad\textbf{(D)}\ 3\qquad\textbf{(E)}\ 3\frac{1}2 </math> |
Revision as of 20:40, 28 July 2011
The area of triangle is 8 square inches. Points
and
are midpoints of congruent segments
and
. Altitude
bisects
. What is the area (in square inches) of the shaded region?