ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If the area of triangle ABC is 136 cm$$^2$$,
then the area of triangle BDE is equal to:

Let the side of the equilateral triangle ABC = a

$$\Rightarrow$$  BC = a

D is the mid-point of BC

$$\Rightarrow$$  BD = $$\frac{a}{2}$$

Side of the equilateral triangle BDE = $$\frac{a}{2}$$

Given, Area of the equilateral triangle ABC = 136 cm$$^2$$

$$\Rightarrow$$  $$\frac{\sqrt{3}}{4}a^2=136$$

$$\therefore\ $$Area of the equilateral triangle BDE = $$\frac{\sqrt{3}}{4}\left(\frac{a}{2}\right)^2$$

$$=\frac{\sqrt{3}}{4}\times\frac{a^2}{4}$$

$$=\frac{1}{4}\times\frac{\sqrt{3}a^2}{4}$$

$$=\frac{1}{4}\times136$$

$$=$$ 34 cm$$^2$$

Hence, the correct answer is Option D