Here,
Let refer to the diagram

ABC is equilateral \(\triangle\)

AD is the height of the \(\triangle\) = 8

For the \(\triangle\) ADC

\(\angle CAD = 30\)
\(\angle ADC = 90\)
\(\angle DCA = 60\)

It is a 30 -60-90 \(\triangle \) and the sides are distributed in the ratio \(1\) : \(\sqrt{3}\) : \(2\)

since, the height AD = 8, hence the sides are distributed as

\(\frac{8}{(\sqrt{3})}\) : \(8\) : \(\frac{16}{(\sqrt{3})}\)

i.e one side of the equilateral \(\triangle\) = \(\frac{16}{(\sqrt{3})}\)

Area of equilateral \(\triangle\) = \(\frac{(\sqrt 3 * {side}^2)}{4}\) =\(\frac{\sqrt 3 * ({\frac {16}{\sqrt3}})^2}{4}\) = 37 (approx)

Now, Area of the circle of radius '7' = \(\pi * {radius}^2 \) = \(\pi *49\) = 154

Therefore, Area of the shaded region = 154 - 37 = 117

QTY A > QTY B