Question:
Diagonals of parallelogram are $6$ and $8$ cm. If one side is $5$ cm, then area of parallelogram is ?
My attempt:
Construct $AH$ perpendicular to base.
Let $DB = 6 cm$ and $AC = 6cm$. Since diagonals of parallelogram bisect each other $AO = OC = 4 cm$ and $OB = OD = 3cm$. But, I don't know where to proceed from where. I have an instinct that probably the AH segment will be used in the solution but I can't just connect to the solution.
Thus, I need help in this problem (hints are most welcome!)
Best Answer
Hint: $(3,4,5)$ is a Pythagorean triple.
If it wasn't a Pythagorean triple, you could use Heron's formula to get the area of triangle $OAD$, and then use the fact that triangles $OAD$ and $ODC$ have the same area: equal base ($AO=OC$) and equal height (perpendicular distance of $D$ from $AC$).