Answer:
13
Step-by-step explanation:
First, find the lengths of all the sides. We can use pythagorean theorem or the distance formula to find this.
Let's find the length of AD using the pythagorean theorem, which states that a^2 + b^2 = c^2. We know a and b, which is 4 and 1.
Put these into the equation, and 16+1=c^2, or 17=c^2. So AD = [tex]\sqrt{17}[/tex] .
Now let's find AB using pythagorean theorem as well. a and b are 1 and 3, so 1+9=c^2, or c^2=10. So AB = [tex]\sqrt{10}[/tex].
Now multiply AB by AD (area of parallelogram is A=BH).
(AD) (AB) = [tex]\sqrt{170}[/tex]
Put this into any calculator and you will find that [tex]\sqrt{170}[/tex] is equal to approximately 13.038. This is close enough to 13, so the answer is 13, or option A.
