What is the formula for the area of a triangle?

• A. base × height
• B. (base × height) / 2
• C. base + height
• D. base + height / 2

Answer: (B)

The formula for the area of a triangle is derived from the fundamental properties of triangles and the relationship between their dimensions. To find the area, you need to account for both the base of the triangle and its height.

When calculating the area, the base represents one side of the triangle, and the height is measured perpendicular to that base from the opposite vertex. The reasoning behind the formula involves understanding that a triangle essentially occupies half the space of a rectangle that contains the same base and height.

Thus, the area is given by multiplying the base and the height together to find the area of the rectangle, and then dividing that product by two to account for the fact that the triangle only occupies half of that space. This leads to the formula ((\text{base} \times \text{height}) / 2).

This is why the choice that states this formula is correct. The other options do not accurately represent how the area of a triangle is calculated, either by missing the division by two or presenting operations that don't pertain to area calculation.