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 a triangular cross-section, you can use the formula: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] In this case, the base is \( 4 \) units and the height is \( 3 \) units. Plugging in those values, we get: \[ \text{Area} = \frac{1}{2} \times 4 \times 3 = \frac{12}{2} = 6 \text{ square units} \] So, the area of one triangular cross-section is \( 6 \) square units! Triangles are the building blocks of geometry and have a fascinating history dating back to ancient civilizations! The Greeks studied them extensively, using them as a basis for understanding more complex shapes and figures. Archimedes, for instance, made contributions to the properties of triangles, which laid the groundwork for later developments in geometry. Speaking of triangles, they’re everywhere in real life! Whether you’re looking at highway signs, the structure of roofs, or even the strength of bridges, triangles provide stability and efficiency. Next time you drive under a bridge or see a pyramid, remember that those strong shapes are rooted in triangle geometry!