Given: ab ∥ dc de ⊥ ab , ad = bc m∠adc = 134° ad = 40, dc = 32 find: area of abcd

Step-by-step explanation:

The formula to calculate the area of trapezoid is:

Where "B" is the long base, "b" is the short base and "h"  is the height.

1. First we need to find the height DE:

- Since:

We can find . This is:

 - Observe in the second figure that the triangles EAD and FDA are equal. Then:

- Use the Trigonometric Identity .

In this case:

Then:

2.Use the Trigonometric Identity to find the lenght AE, which is equal to the lenght GB

In this case:

Then:

- Therefore, the large base AB is:

- Now we can substitute values into the formula and calculate the aera of the trapezoid ABCD. This is:

it has the same slope and a different y-intercept

hope this : )