Calculate Triangle ABC Area in Cuboid with Volume 120 cm³ and Side 4 cm

To solve this problem, we will derive the dimensions of the cuboid using the given volume and side BK, and then find the area of triangle ABC.

We start with the given information:
- Volume of the cuboid: $120 \, \text{cm}^3$
- Side $BK = 4 \, \text{cm}$

The volume formula of the cuboid is:
$V = l \times w \times h = 120 \, \text{cm}^3$

We assume $BK = h = 4 \, \text{cm}$, leading to:
$l \times w \times 4 = 120$
$l \times w = \frac{120}{4} = 30$

Now, to get the area of triangle ABC, which forms a right triangle with sides $l$ and $w$ being the base and height, respectively, we use:
$A = \frac{1}{2} \times l \times w = \frac{1}{2} \times 30 = 15 \, \text{cm}^2$

Thus, the area of triangle ABC is $15 \, \text{cm}^2$.