Answer :

Let ABC be a triangle with sides AB = 26 cm, BC = 28 cm, CA = 30 cm



Now, we know that,

$s=\frac{AB+BC+CA}{2}$
$?$ $s=\frac{26+28+30}{2}=\frac{84}{2}=42cm$

Now, Area of triangle
= $\sqrt{42(42?26)(42?28)(42?30)}$
(Since, Heron's formula [area = $\sqrt{s(s?a)(s?b)(s?c)}$])

= $\sqrt{42\times 16\times 14\times 12}$
= $\sqrt{7\times 6\times 4\times 4\times 2\times 7\times 2\times 6}$
= $7\times 6\times 4\times 2{cm}^2$
= $336{cm}^2$ ...(i)

We know that,

Area of parallelogram = Base × Height ...(ii)

We also have,
Area of parallelogram = Area of $\mathrm{?}ABC$ ...(Given)

Thus, from (i) and (ii),

$?$ Base × Height = 336
$?$ 28 × Height = 336 ...(Given)
$?$ Height = 12cm

Therefore, the height of the parallelogram is 12cm.