Which expression is a correct formula for the area of a triangle in terms of base and height?

Which expression is a correct formula for the area of a triangle in terms of base and height?

• A. A = b h
• B. A = b + h
• C. A = s^2
• D. A = 1/2 b h

Answer: (D)

For a triangle, area comes from multiplying its base by its height, then taking half of that product. The height is the perpendicular distance from the base to the opposite vertex, and this half-factor reflects that a triangle with the same base and height fits exactly into half of the corresponding rectangle. So the area formula is A = (1/2) × base × height, written as A = (1/2) b h. The product bh would give the area of a rectangle with the same base and height, not a triangle; adding base and height isn’t a meaningful measure for area; and squaring a length gives the area of a square, not a triangle. Hence A = 1/2 b h is the correct expression.

For a triangle, area comes from multiplying its base by its height, then taking half of that product. The height is the perpendicular distance from the base to the opposite vertex, and this half-factor reflects that a triangle with the same base and height fits exactly into half of the corresponding rectangle. So the area formula is A = (1/2) × base × height, written as A = (1/2) b h. The product bh would give the area of a rectangle with the same base and height, not a triangle; adding base and height isn’t a meaningful measure for area; and squaring a length gives the area of a square, not a triangle. Hence A = 1/2 b h is the correct expression.