Difference between revisions of "1991 AJHSME Problems/Problem 10"
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== Problem 10 == | == Problem 10 == | ||
| − | |||
| − | <math> \ | + | The area in square units of the region enclosed by parallelogram <math>ABCD</math> is |
| + | |||
| + | <asy> | ||
| + | unitsize(24); | ||
| + | pair A,B,C,D; | ||
| + | A=(-1,0); B=(0,2); C=(4,2); D=(3,0); | ||
| + | draw(A--B--C--D); draw((0,-1)--(0,3)); draw((-2,0)--(6,0)); | ||
| + | draw((-.25,2.75)--(0,3)--(.25,2.75)); draw((5.75,.25)--(6,0)--(5.75,-.25)); | ||
| + | dot(origin); dot(A); dot(B); dot(C); dot(D); label("$y$",(0,3),N); label("$x$",(6,0),E); | ||
| + | label("$(0,0)$",origin,SE); label("$D (3,0)$",D,SE); label("$C (4,2)$",C,NE); | ||
| + | label("$A$",A,SW); label("$B$",B,NW); | ||
| + | </asy> | ||
| + | |||
| + | <math>\text{(A)}\ 6 \qquad \text{(B)}\ 8 \qquad \text{(C)}\ 12 \qquad \text{(D)}\ 15 \qquad \text{(E)}\ 18</math> | ||
==Solution== | ==Solution== | ||
| − | The base is <math>\overline{BC}=4</math>. The height has a length of the difference of the y-coordinates of A and B, which is 2. Therefore the area is <math>4\cdot 2=8\Rightarrow \boxed{\mathrm{ | + | |
| + | The base is <math>\overline{BC}=4</math>. The height has a length of the difference of the y-coordinates of A and B, which is 2. Therefore the area is <math>4\cdot 2=8\Rightarrow \boxed{\mathrm{B}</math>. | ||
| + | |||
| + | ==See Also== | ||
| + | |||
| + | {{AJHSME box|year=1991|num-b=9|num-a=11}} | ||
| + | [[Category:Introductory Geometry Problems]] | ||
Revision as of 21:18, 7 August 2009
Problem 10
The area in square units of the region enclosed by parallelogram 
is
![[asy] unitsize(24); pair A,B,C,D; A=(-1,0); B=(0,2); C=(4,2); D=(3,0); draw(A--B--C--D); draw((0,-1)--(0,3)); draw((-2,0)--(6,0)); draw((-.25,2.75)--(0,3)--(.25,2.75)); draw((5.75,.25)--(6,0)--(5.75,-.25)); dot(origin); dot(A); dot(B); dot(C); dot(D); label("$y$",(0,3),N); label("$x$",(6,0),E); label("$(0,0)$",origin,SE); label("$D (3,0)$",D,SE); label("$C (4,2)$",C,NE); label("$A$",A,SW); label("$B$",B,NW); [/asy]](http://latex.artofproblemsolving.com/0/0/6/006625b37683a704cc02bcf460b1e73c2e0ecc24.png)
Solution
The base is 
. The height has a length of the difference of the y-coordinates of A and B, which is 2. Therefore the area is $4\cdot 2=8\Rightarrow \boxed{\mathrm{B}$ (Error compiling LaTeX. Unknown error_msg).
See Also
| 1991 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Problem 11 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
