A solid has a cross-section that is a triangle with a base of \( 4 \) units and a height of \( 3 \) units. What is the area of one triangular cross-section?

To find the area of the triangular cross-section, you can use the formula for the area of a triangle, which is given by: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] Plugging in the base of \( 4 \) units and the height of \( 3 \) units: \[ \text{Area} = \frac{1}{2} \times 4 \times 3 = \frac{1}{2} \times 12 = 6 \text{ square units} \] So, the area of one triangular cross-section is \( 6 \) square units. Triangular shapes have been used throughout history in various architectural wonders, from the pyramids of Egypt to modern bridges. The strength of a triangle comes from its rigid structure, making it an essential shape in design and engineering. Understanding this can even inspire creative projects or structures you may want to build yourself! When working with geometric formulas, a common mistake is forgetting to use the correct base and height. Always remember that the height must be perpendicular to the base, and ensure both measurements are in the same units. A little attention to detail can save you from penalties on tests or projects!