A trapezoid ABCD has an area of 24 sq. units. There of its coordinates are
B(1,8) , C(2,3), and D(-6,3) . Find the coordinates of A.
can anybody help me on this problem above please.
1. This problem has no unique solution, because with the given conditions you can draw 6 different trapezoids.
2. See attachment: There are 2 trapezoids in red, 2 trapezoids in blue, 2 trapezoids in green.
3. Take the red trapezoids (that's the simplest case!):
Point A must be situated on a parallel to the x-axis with the equation y = 8.
The area of a trapezoid is calculated by :
,
So you have to solve for :
which yields
So you get 2 different points A: or
4. The next 4 trapezoids are much more difficult to determine.
To begin with, I think that the answer given in your book is wrong.
I think that the wording, 'a trapazoid ABCD', implies that the points should be taken in that order in which case the point A lies between the points B and D (and outside of the triangle BCD).
With that assumption, there seem to be two possible constructions, one where AB is parallel to DC and the other where AD is parallel to CB. The first of these is the easier to deal with.
The triangle BCD has a base of length 8 and a height 5 so its area is 8*5/2=20. That means that the triangle ABD should have an area of 4.
Take AB to be the base of ABD, then its height will be 5 in which case its area will be 5*AB/2 and that has to equal 4.
From that it's easy to calculate the x coordinate of A, (and it agrees with an answer given in an earlier post).
The other possible position for A is more awkward to calculate, and since your book gives only one answer, I would guess that you are not expected to find it.
Hello, rcs!
Is there a typo in the problem?
That would explain their answer.
A trapezoid ABCD has an area of 25 sq. units.
Three of its coordinates are: B(1,8), C(2,3), and D(-6,3) .
Find the coordinates of A.
The problem is not clearly stated.
As earboth pointed out, there are six possible trapezoids.
I assume that the horizontal side is the "base"
. . and
Hence, is in Quadrant 2.
The height isCode:| (x,8) | (1,8) A♥ * * * * ♥B * | * * | * * | * * | * D♥ * * * * * * |* * * * * ♥C (-6,3) | (2,3) | - - - - - - - - - + - - - - - - - - |
The bases are: .
Area of a trapezoid: .
Hence, we have: .
. .
Therefore: .