Answer
Length of each of the equal sides $\approx 9.8$ cm
Work Step by Step
Given, area of the isosceles triangle, 'A' = 24 $cm^{2}$
Angle included by the equal sides, $\theta$ = $\frac{5\pi}{6}$
Let's assume that each of the equal sides is 'a' cm.
We know that-
A = $ \frac{1}{2}$ a b $\sin \theta$
or,
24 = $ \frac{1}{2} \times a \times a \times \sin \frac{5\pi}{6}$
24 = $ \frac{1}{2} \times a^{2} \times \sin \frac{\pi}{6}$
($\frac{\pi}{6}$ is the reference angle for $\frac{5\pi}{6}$
24 = $ \frac{1}{2} \times a^{2} \times \frac{1}{2}$
($\sin\frac{\pi}{6} = \frac{1}{2}$)
i.e. $a^{2}$ = $24\times4$ = 96
i.e. $ a = \sqrt {96} \approx 9.8$ cm
