If momentum ( P ) , area ( A ) and time ( T ) are taken to be the...

Let dimension formula of energy will be

$E = A^{a}T^{b}P^{c}$
$P = M^{1}L^{1}T^{- 1}$
$A = L^{2}$
$T = T^{1}$
$M^{1}L^{2}T^{- 2} = M^{C}L^{2a + c}T^{b - c}$
by comparison $C = 1......... \left(1\right)$
$2a + c = 2...... \left(2\right)$
$b - c = - 2........ \left(3\right)$
$c = 1, a = 1 / 2, b = - 1$
$E = A^{1 / 2}T^{- 1}P^{1}$