Answer:
Area of a parallelogram would be 13.46
Step-by-step explanation:
Since area of a parallelogram is represented by the formula
Area = [tex]\frac{1}{2}[/tex] ([tex](D_{1}*D_{2})[/tex]
Where [tex]D_{1}[/tex] and [tex]D_{2}[/tex] are two diagonals of the given parallelograms.
In the given figure [tex]D_{1}=AC[/tex] and [tex]D_{2}[/tex] = BD
We will find the length of [tex]D_{1}[/tex] and [tex]D_{2}[/tex] first
Since points A and C are (3,6) and (5,1)
So distance AC = [tex]\sqrt{(6-1)^{2}+(3-5)^{2} }[/tex]
= [tex]\sqrt{5^{2}+(-2)^{2}}[/tex]
= [tex]\sqrt{25+4}=\sqrt{29}[/tex]
Since B and D are the points (6, 5) and (2, 2)
So length of BD = [tex]\sqrt{(6-2)^{2}+(5-2)^{2}}[/tex]
BD = [tex]\sqrt{4^{2}+3^{2}}=\sqrt{25}=5[/tex]
Now we will put these values in the formula
Area of parallelogram = [tex]\frac{1}{2}(\sqrt{29})(5)[/tex]
= [tex]\frac{5}{2}[/tex] × [tex]\sqrt{29}[/tex]
= (2.5) (5.385)
= 13.46
