SOLUTION: Find the area of the trapezoid pictured below. A trapezoid is drawn with smaller base labeled 8 units. The larger base is not labeled but has a 40 degree angle on each end. The l

Algebra ->  Surface-area -> SOLUTION: Find the area of the trapezoid pictured below. A trapezoid is drawn with smaller base labeled 8 units. The larger base is not labeled but has a 40 degree angle on each end. The l      Log On


   

Question 110819: Find the area of the trapezoid pictured below.
A trapezoid is drawn with smaller base labeled 8 units. The larger base is not labeled but has a 40 degree angle on each end. The legs of the trapezoid are both labeled 10 units.
83.5 sq. units
96.4 sq. units
70.2 sq. units
100.7 sq. units
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
My only quibble with your excellent description is that a base is the line on the bottom, so you can't have two of them in a trapezoid. Several on-line sites call them bases so I will withdraw my quibble.
Construct a line from one end of the short parallel line perpendicular to the longer parallel line.
we have a right triangle with hyp.=10.
sin(40)=opp/10
opp=sin(40)*10
opp=6.42788
This is the altitude of the trapezoid, also.
cos(40)=adj/10
adj=cos(40)*10=7.66044
This is a portion of the larger parallel line.
There is a similar portion on the other side if a 2nd altitude is constructed at the other end of the smaller parallel line.
So, the length of the larger line is 7.66044+8+7.66044=23.32...
A=average of the parallel lines * altitude
A=((8+23.32...)/2)*6.43...
=15.66...*6.43...
=100.7... sq units
Ed