Answer:
[tex]A=1,720.16\ units^2[/tex]
Step-by-step explanation:
we know that
The area of the trapezoid is equal to
[tex]A=\frac{1}{2}(DC+AB)DE[/tex]
step 1
Find the measure of angle DAE
m∠ADC+m∠DAE=180° -----> by consecutive interior angles
we have
m∠ADC = 134°
substitute
134°+m∠DAE=180°
m∠DAE=180°-134°=46°
step 2
In the right triangle ADE
Find the length side AE
cos(∠DAE)=AE/AD
[tex]AE=cos(46\°)(40)\\AE=27.79\ units[/tex]
step 3
In the right triangle ADE
Find the length side DE
sin(∠DAE)=DE/AD
[tex]DE=sin(46\°)(40)\\DE=28.77\ units[/tex]
step 4
Find the area of ABCD
[tex]A=\frac{1}{2}(DC+AB)DE[/tex]
we have
[tex]DC=32\ units\\AB=DC+2(AE)=32+2(27.79)=87.58\ units\\DE=28.77\ units[/tex]
substitute
[tex]A=\frac{1}{2}(32+87.58)28.77[/tex]
[tex]A=1,720.16\ units^2[/tex]
