Question

The unequal side of an isosceles triangle is 6cmand its perimeter is 24 cm.find its area

Answer 1

the equal sides =24-6/2=18/2=9
height =root 9^2-3^2=81-9=root72=6root2

area=1/2×b×h=1/2×6×6root2=18root2 Ans

Answer 2

Let equal side be x
so 2x + 6 = 24
2x = 24-6 = 18
x = 18/2
x = 9
now using herons formula
$\sqrt{s(s - a)(s - b)(s - c)}$
where a is semi perimeter and a,b and c are sides so semi perimeter= 24/2 = 12
now area =
$\sqrt{12(12 - 9)(12 - 9)(12 - 6)} \\ \sqrt{12 \times 3 \times 3 \times 6} \\ \sqrt{36 \times 18} = 6 \sqrt{18}$
or
$25.455$
hope it helps