Which formula allows for the calculation of the area of a triangle?

Which formula allows for the calculation of the area of a triangle?

• A. (Base × Height)/2
• B. Base × Height
• C. (Base + Height)/2
• D. Base × Height × 2

Answer: (A)

The formula for calculating the area of a triangle is indeed based on the relationship between the triangle's base and height. The area can be determined using the formula (Base × Height)/2. This reflects the fact that the area of a triangle is essentially half the area of a rectangle that would encompass it. In a rectangle, the area is calculated by multiplying the base by the height directly. Since a triangle occupies half of that rectangle's space when the base and height are the same, dividing the product of the base and height by two precisely gives the correct area. This understanding is fundamental in geometry and applies to any triangle, regardless of its specific shape or angles, as long as the base and height are perpendicular to each other. Other options do not represent the correct method for calculating the area of a triangle. The multiplication of base by height without division fails to account for the triangular shape. Also, simple additions or multiplications by two introduce inaccuracies in determining the area, as they do not consider the proportional relationship inherent to triangles. Therefore, the correct formula effectively captures the geometric properties necessary for proper area calculation.

The formula for calculating the area of a triangle is indeed based on the relationship between the triangle's base and height. The area can be determined using the formula (Base × Height)/2. This reflects the fact that the area of a triangle is essentially half the area of a rectangle that would encompass it. In a rectangle, the area is calculated by multiplying the base by the height directly. Since a triangle occupies half of that rectangle's space when the base and height are the same, dividing the product of the base and height by two precisely gives the correct area. This understanding is fundamental in geometry and applies to any triangle, regardless of its specific shape or angles, as long as the base and height are perpendicular to each other.

Other options do not represent the correct method for calculating the area of a triangle. The multiplication of base by height without division fails to account for the triangular shape. Also, simple additions or multiplications by two introduce inaccuracies in determining the area, as they do not consider the proportional relationship inherent to triangles. Therefore, the correct formula effectively captures the geometric properties necessary for proper area calculation.