How can piecewise linear functions be multiplied analytically?

Hello,

The result to be obtained

Can we somehow show the result of the power p (t) (i.e. the multiplication of v (t) with i (t)) in an analytically way, apart from the graphical solution?

Or, how can piecewise linear functions be multiplied analytically and the result can be shown, as above figure shown?

(

)

Thanks.