# Find the area of the $\Delta$ if $a=18,b=24,c=30$

$(a)\;216sq.units\qquad(b)\;215sq.units\qquad(c)\;214sq.units\qquad(d)\;210sq.units$

We know that
$\Delta=\sqrt{s(s-a)(s-b)(s-c)}$
$\quad=\sqrt{36(36-18)(36-24)(36-30)}$
$\quad=\sqrt{36\times 18\times 12\times 6}$
$\quad=\sqrt{2\times 18\times 18\times 6\times 2\times 6}$
$\quad=\sqrt{46656}$
$\quad=216$sq.units
Hence (a) is the correct answer.