Two equilateral triangles of side $$10\sqrt{3}$$ cm are joined to form a quadrilateral. What is the altitude of the quadrilateral?

Given that  $$10\sqrt{3}$$ cm

We know the area of equilateral triangle = $$ \frac{\sqrt {3}} {4} a^2 $$   ...... Eq (1)

and on the $$\triangle DCB   is   also   given = \frac{1}{2} \times a \times h $$   ...... Eq (2) 

then Eq(1) = Eq (2)

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

$$\Rightarrow h =  \frac{\sqrt{3}} {2} a $$

$$\Rightarrow h = \frac{\sqrt{3}} {2} \times 10\sqrt{3}$$

$$\Rightarrow h = 15 cm Ans