Question

Given: AB ∥ DC

Answer 1

Answer:

$A=1,720.16\ units^2$

Step-by-step explanation:

we know that

The area of the trapezoid is equal to

$A=\frac{1}{2}(DC+AB)DE$

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

$AE=cos(46\°)(40)\\AE=27.79\ units$

step 3

In the right triangle ADE

Find the length side DE

sin(∠DAE)=DE/AD

$DE=sin(46\°)(40)\\DE=28.77\ units$

step 4

Find the area of ABCD

$A=\frac{1}{2}(DC+AB)DE$

we have

$DC=32\ units\\AB=DC+2(AE)=32+2(27.79)=87.58\ units\\DE=28.77\ units$

substitute

$A=\frac{1}{2}(32+87.58)28.77$

$A=1,720.16\ units^2$