ABC is an equilateral triangle, having a side length of 4 cm . Knowing that forces of magnitudes \( 150 \mathrm{~N}, 400 \mathrm{~N} \), and 50 N are acting as shown in the figure, determine the sum of the moments of these forces about the point of intersection of the triangle's medians, rounded to two decimal places. \( \begin{array}{lll}\text { (a) } 692.82 \mathrm{~N} . \mathrm{cm} & \text { (b) } 653.4 \mathrm{N.cm} \\ \text { (c) } 700 \mathrm{N.cm} & \text { (d) } 721.8 \mathrm{N.cm}\end{array} \)

First, let's dive into the calculations! The centroid of an equilateral triangle is where the medians intersect, and it divides each median into a 2:1 ratio. For side length 4 cm, the height \( h \) of triangle ABC can be calculated using the formula \( h = \frac{\sqrt{3}}{2} \times \text{side} \). For forces acting on different points, moments are calculated as \( \text{Force} \times \text{Distance} \). Ensure you take the distance from the line of action of the force to the centroid. After performing the necessary calculations, you can sum the moments to find the total. A neat approach to remembering how to compute moments is visualizing them as "twisting forces." When multiple forces act on a structure, visualize each of their effects as a small twist - that can help avoid confusion! Also, don't forget to keep an eye on the angle between the force and the lever arm, as it adjusts your moment calculation!