Which formula represents the area of a triangle?

Which formula represents the area of a triangle?

• A. base × height
• B. 1/2 × base × height
• C. base + height
• D. base × height ÷ 2

Answer: (B)

The formula for the area of a triangle is derived from the concept of base and height. To find the area, you take the base of the triangle and multiply it by the height, which is the perpendicular distance from the base to the opposite vertex. However, since a triangle is essentially half of a rectangle formed by doubling the area of the triangle, the formula includes a factor of one-half. Thus, when you multiply the base by the height and then divide by two, you effectively calculate the area of the triangle. This makes the correct formula for the area of a triangle \( \frac{1}{2} \times \text{base} \times \text{height} \). This approach clarifies why the other options do not correctly represent the area of a triangle. Simply multiplying the base by height gives the area of a rectangle instead. Adding the base and height does not yield a meaningful geometric measurement. Finally, although dividing the product of base and height by 2 achieves the correct area, it does not include the necessary fraction, making it incomplete compared to the standard area formula, which clearly signifies that a triangle's area is half that of a rectangle with the same base and height.

The formula for the area of a triangle is derived from the concept of base and height. To find the area, you take the base of the triangle and multiply it by the height, which is the perpendicular distance from the base to the opposite vertex. However, since a triangle is essentially half of a rectangle formed by doubling the area of the triangle, the formula includes a factor of one-half.

Thus, when you multiply the base by the height and then divide by two, you effectively calculate the area of the triangle. This makes the correct formula for the area of a triangle ( \frac{1}{2} \times \text{base} \times \text{height} ).

This approach clarifies why the other options do not correctly represent the area of a triangle. Simply multiplying the base by height gives the area of a rectangle instead. Adding the base and height does not yield a meaningful geometric measurement. Finally, although dividing the product of base and height by 2 achieves the correct area, it does not include the necessary fraction, making it incomplete compared to the standard area formula, which clearly signifies that a triangle's area is half that of a rectangle with the same base and height.