If a rectangle has base B and height H and a triangle sits on the rectangle with its vertex touching the opposite side, what is the area of the triangle in terms of B and H?

If a rectangle has base B and height H and a triangle sits on the rectangle with its vertex touching the opposite side, what is the area of the triangle in terms of B and H?

• A. BH
• B. BH/2
• C. 2BH
• D. BH/4

Answer: (B)

The area of a triangle is half the product of its base and its height. Here, the triangle’s base sits along the rectangle’s base, so its base length is B. Its vertex touches the opposite side of the rectangle, meaning the perpendicular distance from the base to the vertex is the rectangle’s height, H. Multiply: (1/2) × B × H = BH/2. So the area is BH/2.

The area of a triangle is half the product of its base and its height. Here, the triangle’s base sits along the rectangle’s base, so its base length is B. Its vertex touches the opposite side of the rectangle, meaning the perpendicular distance from the base to the vertex is the rectangle’s height, H. Multiply: (1/2) × B × H = BH/2. So the area is BH/2.