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16 Aug 2021, 09:11
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
31% (02:24) correct
69%
(01:54)
wrong
based on 67
sessions
History
Date
Time
Result
Not Attempted Yet
In the xy-plane, the five vertices of a pentagon are located at (a, b), (a + 6, b), (a − 2, b + 5), (a + 9, b + 5) and (c, d).
What is the area of the pentagon?
1) c = a + 5
2) d = b + 8
What is the area of the pentagon?
1) c = a + 5
2) d = b + 8
16 Aug 2021, 22:10
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sjuniv32
All 8 answers on timers are wrong. I am sure most would have clicked C as the answer, meaning we tend to fall for C trap without analyzing the information
The pentagon is fixed, so if we take a and b as 0 each, that is (a,b) is the origin, the points are -
(a, b), (a + 6, b), (a − 2, b + 5), (a + 9, b + 5) and (c, d) : A(0,0), B(6,0), C(-2,5), D(9,5) and E(c,d).
Now, it is easy to believe that we require value of c and d.
But if you draw the figure, you can fix A, B, C and D as shown in attached figure.
If we join C and D, line CD is parallel to line AB.
Area of trapezium can be found.
We have to fix E. It does not matter where E is as far as x-coord is concerned, we just require the height of triangle CDE to get its area. And the height is nothing but the y-coord.
1) c = a + 5=5
We require y-coords.
Insuff
2) d = b + 8=8
exactly what we were looking for.
Sufficient
B
Attachments
pentagon.png [ 18.15 KiB | Viewed 2006 times ]
16 Aug 2021, 22:35
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sjuniv32
i would first take you through my thought process so many variables intially we feel as though the problem is not realistically possible
however we should keep in mind that they are just making us calculate the area which means finding a host of perpendiculars and we can basically divide the area into various section and find the area
in simpler terms we are more intrested in knowing about the y- coordinate will help us solve the problem
1) c = a + 5
eqn of x-coordinate we cannot realistically figure the area
2) d = b + 8
clearly what we were looking for and we got an eqn in figuring out the y coordinate
Therefore IMO B
