Given: abcd ∥gram, bk ⊥ ad , ab ⊥ bd ab=6, ak=3 find: m∠a, bk, area of abcd

1. Consider right triangle ABK. In this triangle AB is the hypotenuse, BK and AK are legs. By the Pythagorean theorem,

2. Use the definition of

Then

3. Consider right triangle ABD. In this triangle AD is the hypotenuse, AB and BD are legs. Since   then

The leg that is opposite to the angle of 30° is half of the hypotenuse, so

4. The area of parallelogram aBCD is

for the points

step-by-step explanation: