The diagonal of a square is equal to the side of an equilateral triangle. If the area of the square is $153\text{sq cm}$, what is the area of the equilateral triangle?

Let the side of the square be $s$ and its diagonal be $d$.The area of a square in terms of its diagonal is given by:
$$\text{Area of square}=\frac{d^2}{2}$$
Given that the area of the square is $153\text{sq cm}$:
$$\frac{d^2}{2}=153⟹d^2=306$$
According to the question, the side of the equilateral triangle ($a$) is equal to the diagonal of the square ($d$):
$$a=d⟹a^2=d^2=306$$
The formula for the area of an equilateral triangle is:
$$\text{Area}=\frac{\sqrt{3}}{4}{a}^2$$
Substitute $a^2=306$:
$$\text{Area}=\frac{\sqrt{3}}{4}\times 306=\frac{306}{4}\sqrt{3}=\frac{153\sqrt{3}}{2}\text{sq cm}$$