Questions on Geometry: Polygons answered by real tutors!

You can put this solution on YOUR website!
Let's name the parallel sides as a[1] =9inches

and

And the non parallel sides as "c=?" and "d=?".
Before I proceed farther, I suggest you draw it on your own while we discuss it by words so you can follow better (just a suggestion).
.
Now from that starting point and also the endpoint of that 9 inches which is a[1]

, draw a line all the way down to b[1]

which is perpendicular right? --> mark these lines as "h" (for height),likewise the 2 lines are parallel, and that line inside these parallel lines on b[1]

also measures 9 inches right (of course) ---> mark it a[2]

.
Now you have remaining length of 3 inches, b[1]-a[2]=12-9=3

And these 3 inches will be cut into half, 1-1/2" on one side, likewise 1-1/2" on the other. Why? Because you have opposite similar 65 deg angle right? (If not the same angle, the length won't be the same)
The 1-1/2" length mark one side as b[2]

and the other as b[3]

.
Can you follow still?
Now, side "c", "h" and b[2]

forms a right triangle (if you mark them properly) with angle 65 deg. To get "c",
cos65=b[2]/c

= 1.5/cos65
c=3.55 inches = d -------------> length of the non parallel sides
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For area in the trapezoid,
A=1/2(h) (a[1]+b[1])

To get "h", sin65=h/c

h=(sin65)(3.55)=3.22 inches
Therefore,
A=(1/2)(3.22){9+12}
A=33.81 sq inches
Thank you,
Jojo