Question

The figure below shows trapezoid ABCD on a coordinate plane. Which of the following expressions represents the area of this figure in square units?

a.148
b.74
c.37
d.18
https://media.glynlyon.com/g_geo_ccss_2013/9/img_geo_9_5a_graphing_6.gif

Answer 1

@elementwielder

Answer 2

im sorry but i dont really have time right now to answer questions as i am studying for my final exams tomorrow

Answer 3

I's no problem, good luck!

Answer 4

It's

Answer 5

thank you and to you as well @Whitemonsterbunny17 please help

Answer 6

@Embryo

Answer 7

The area of a trapezoid is given by\[Area=\frac{ a+b }{ 2 }h\]where a and b are parallel lines segments, and "h" is the height from "a" to "b", now because you have a graph, you have points, so you need to calculate the distances between the different points, i'll tell you this, "a" in that formula is the distance from point B to C, "b" is the distance from point A to D, and the height "h" is the distance from point B to E.
After you find all those you plug them into the Area formula

Answer 8

I got from A to D is 333 units. From D to C is 74 units. From C to B is 37 units. From B to A is 74 units. @Embryo

Answer 9

Alrighty, so from the numbers you got (i didn't calculate it, i trust you), the way the variables in the Area of a trapezoid equation as i stated should be given these values,
a=37, b=333, and then h=not what you got
h should be the distance from point B to point E, not B to A

Answer 10

unless you just typed A and meant E, not sure

Answer 11

For B to E I got 37

Answer 12

alrighty, so carrying on from the previous stuff,
a=37,b=333, and h =37, plugging those into the area formula we get\[Area=\frac{ 37+333 }{ 2 }37\]which is an incredibly large number, are you surrrreeeee, i'll go ahead and calculate this as well, because these are some big numbers

Answer 13

i think you took the distances wrong, because if you think about it, you can't have 37 units in between any of those points

Answer 14

you must have forgotten to take the square root

Answer 15

yup, okay, so you forgot to take the square root of all the distances, after you take the square roots, you should get the answer\[Area=\frac{ \sqrt{37}+\sqrt{333} }{ 2 }\sqrt{37}=74\]that's good, you took the distances correctly, but forgot to take the square root, just remember that part and you'll be fine

Answer 16

Okay thank you. I have one more that I don't understand. It's the same figure and it wants the area of EBCD.

Answer 17

go ahead and ask it, i'll help if i can

Answer 18

oh wait lol, it's the same figure okay XD

Answer 19

lol ya

Answer 20

Alrighty, well one way to approach this problem now, is to check one thing, if Line AB is equal in length to Line CD, if they are, then you can calculate the area of the square that i will attach, labeled CBEX, and add the area of the triangle BAE

Answer 21

I have to go do something but I will be done in about 25 minutes. Will you still be available?

Answer 22

I will, see you when you return

Answer 23

Hi I'm sorry it took longer than i thought last night and when I was done it was really late @Embryo

Answer 24

Ah it's totally fine

Answer 25

Could you help me with that problem now?

Answer 26

Of course, ask away

Answer 27

The one you started to help me with last night

Answer 28

ahh oh yeah sorry, forgot lol, one sec to refresh myself on the question

Answer 29

Alrighty, well one way to approach this problem now, is to check one thing, if Line AB is equal in length to Line CD, if they are, then you can calculate the area of the square that i will attach, labeled CBEX, and add the area of the triangle BAE

Answer 30

What did you say the measurement for BE was?

Answer 31

Was is sqrt 37?

Answer 32

yup

Answer 33

So what would my equation look like?

Answer 34

The equation for the area of the square? is that what you mean?

Answer 35

ya

Answer 36

Excuse me, i shouldn't say that it's a square, we don't exactly know if all sides are equal, so we need to calculate the length of at least 2 sides to know the area of that "rectangle," we can do that by finding the length of BE as we found to be sqrt{37} and multiplying it by the length of BC which you found to be sqrt{37}, so hey, would you look at that, it does happen to be a square, so the area is easy to find then

Answer 37

ok give me a sec

Answer 38

I got 37 @Embryo

Answer 39

SO when you divide it the final answer is 37 right?

Answer 40

Yes, 37, that should be the area of that square (now that we know it is indeed a square), but we're not done yet, you need to find the area of that triangle CXD that i made the picture for, but since we don't actually know where point X is, we have to do something a little different

Answer 41

like i said earlier, you need to find the length of CD and BA, and figure out if they are equal (which they should be), go ahead and see if they are

Answer 42

I am sorry if this seems like a lot to do for one problem, but everything i'm telling you is necessary to get the right answer

Answer 43

So the servers crashed and idk when you'll be back to finish this problem, but fear not, i will be here to answer your question till the end, but if i don't respond fast, it's probably because i'm eating dinner

Answer 44

Okay I'm so tired of this problem. Can you please quickly help me finish this @Embryo

Answer 45

The thought process for calculating the area of BCDE is like this, you an obviously make a square from the trapezoid and calculate the area of that, but the problem is that we don't know what point X is at in the drawing i gave you (i'll attach it again), so we need to figure out if BA = CD, it that is true, then we know that the area of triangle BAE=CDX then we can just add up the area of the square BCDE and the triangle BAE which would give you the area of BCXE

Answer 46

yes please finish it because i got so many notifications

Answer 47

Since we found out earlier that BCXE is indeed a square, we can calculate the area of the square to be the length of BC^2

Answer 48

And yes, i would love to finish it as well

Answer 49

thanks