I have four questions:
1. The area of trapezoid ABCD is 60. One base is 4 units longer than the other, and the height of the trapezoid is 5. Find the length of the median of the trapezoid.
2. In trapezoid ABCD, line BC is parallel to line AD, angle ABD = 105 degrees, angle A = 43 degrees, and angle C = 141 degrees. Find angle CBD, in degrees.
3. The bases of trapezoid ABCD are lines AB and CD. Let M be the midpoint of line AD. If the areas of triangles ABM and CDM are 5 and 17 respectively, then find the area of trapezoid ABCD.
4. Let ABCD be a parallelogram. Extend line BC past B to F, and let E be the intersection of lines AB and DF. If the areas of triangles BEF and ADE are 1 and 9, respectively, find the area of parallelogram ABCD.
9 answers
What are your thoughts on this problem? What have you tried so far? Try not to ask questions in your homework, or what you need these for because it is considered cheating unless you show what you have tried.
I'm sick and tired of your cheating on our homework problems! Your account has been deactivated.
Man leave the boy alone GOD
People are always bullying these days, what you could have said s "Hey man this website is for helping each other not cheating so can you try and show us your thoughts." Not "I'm sick and tired of your cheating on our homework problems! Your account has been deactivated." DO YOU UNDERSTAND ME
How would you feel if you got bullied. Think about it.
People are always bullying these days, what you could have said s "Hey man this website is for helping each other not cheating so can you try and show us your thoughts." Not "I'm sick and tired of your cheating on our homework problems! Your account has been deactivated." DO YOU UNDERSTAND ME
How would you feel if you got bullied. Think about it.
Yes, I agree. However, HOW IS IT POSSIBLE THAT AOPS CAN TRACK YOUR COMPUTER?! They have said that they can and will see your IP address, except I'm skeptical about their ability to do that.
IKR He's Stupid
lol im questioning if the guy is even from AOPS
Excuse me if you are questioning our authority then your accounts can be deactivated to. We can resolve this issue with a simple apology.
Go ahead & deactivate half of your users because around that much doesn't care about it on your public board, oh yeah including me.
I'm 6 years too late, but...
1. Let the median of the trapezoid be $m$. Then by the formula for the area of the trapezoid,
\[5m = 60,\]so $m = \boxed{12}$. (The fact that one base is 4 units longer than the other is irrelevant.)
2. (This is written using different variables, but I think you can figure it out) Since $\overline{XY}$ and $\overline{WZ}$ are parallel, we have $\angle WXY = 180^\circ - \angle W = 180^\circ - 43^\circ = 137^\circ$.
[asy]
unitsize(1.5 cm);
pair A, B, C, D;
A = (0,0);
B = (0.5,1);
C = (2,1);
D = (3,0);
draw(A--B--C--D--cycle);
draw(B--D);
label("$W$", A, SW);
label("$X$", B, NW);
label("$Y$", C, NE);
label("$Z$", D, SE);
[/asy]
Then $\angle YXZ = \angle WXY - \angle WXZ = 137^\circ - 105^\circ = \boxed{32^\circ}$.
Also, basing off the unprofessionalism the AoPS account displayed, it isn't actually the official account. So rest assured, no ones account will ever be deactivated. You pay for it, they aren't going to kick you.
1. Let the median of the trapezoid be $m$. Then by the formula for the area of the trapezoid,
\[5m = 60,\]so $m = \boxed{12}$. (The fact that one base is 4 units longer than the other is irrelevant.)
2. (This is written using different variables, but I think you can figure it out) Since $\overline{XY}$ and $\overline{WZ}$ are parallel, we have $\angle WXY = 180^\circ - \angle W = 180^\circ - 43^\circ = 137^\circ$.
[asy]
unitsize(1.5 cm);
pair A, B, C, D;
A = (0,0);
B = (0.5,1);
C = (2,1);
D = (3,0);
draw(A--B--C--D--cycle);
draw(B--D);
label("$W$", A, SW);
label("$X$", B, NW);
label("$Y$", C, NE);
label("$Z$", D, SE);
[/asy]
Then $\angle YXZ = \angle WXY - \angle WXZ = 137^\circ - 105^\circ = \boxed{32^\circ}$.
Also, basing off the unprofessionalism the AoPS account displayed, it isn't actually the official account. So rest assured, no ones account will ever be deactivated. You pay for it, they aren't going to kick you.
10 answers