Final answer:
The area of the triangle, when the base is 10 centimeters and the height is 20 centimeters, will be 100 square centimeters as per the formula A = 1/2 × base × height.
Step-by-step explanation:
The question pertains to the concept of direct variation and the area of a triangle, specifically how the area changes with respect to its base and height. Since the area varies jointly with the base and the height, it can be represented by the formula A = 1/2 × b × h, where A is the area, b is the base, and h is the height of the triangle.
Given that the area is 75 square centimeters with a base of 10 centimeters, to determine the new area when the base is unchanged, and the height is increased to 20 centimeters, we simply plug in these values into the given formula. We calculate: A = 1/2 × 10 cm × 20 cm
Transformation of the formula reduces it to: A = 5 cm × 20 cm = 100 cm2, which means the new area will be 100 square centimeters.