What is the formula for the area of a triangle?

• A. Area = base + height
• B. Area = base * height
• C. Area = 1/2 * base * height
• D. Area = base / height

Answer: (C)

The formula for the area of a triangle is indeed given by the expression that involves one-half times the base multiplied by the height, which is represented as 1/2 * base * height.

To understand why this formula works, consider that the area of any shape can be thought of as the amount of space it occupies. For triangles, the relationship between the base and height helps in deriving the area. The height is a perpendicular line segment from the vertex of the triangle opposite the base down to the line that contains the base.

If you were to take a triangle and replicate it, you could form a rectangle. A rectangle with the same base and height will have an area calculated as base * height. However, since a triangle is only half of that rectangle, the area of the triangle is therefore one-half the area of the rectangle, leading us to the formula 1/2 * base * height.

This geometric reasoning solidifies why the correct choice accurately represents the area of a triangle.