If the base of a triangle is doubled and the height remains the same, how does t

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Question: If the base of a triangle is doubled and the height remains the same, how does the area change?

Options:

Correct Answer: It doubles

Solution:

Area = 1/2 * base * height; if base is doubled, area = 1/2 * (2 * base) * height = 2 * (1/2 * base * height).

If the base of a triangle is doubled and the height remains the same, how does the area change?

If the base of a triangle is doubled and the height remains the same, how does the area change?

Step 1: Understand the formula for the area of a triangle, which is Area = 1/2 * base * height.
Step 2: Identify the original base of the triangle and the height. Let's call the original base 'base' and the height 'height'.
Step 3: If the base is doubled, the new base becomes '2 * base'.
Step 4: Substitute the new base into the area formula: Area = 1/2 * (2 * base) * height.
Step 5: Simplify the equation: Area = 1/2 * 2 * base * height, which equals Area = base * height.
Step 6: Compare the new area (base * height) with the original area (1/2 * base * height).
Step 7: Notice that the new area is twice the original area, meaning the area has doubled.

Area of a Triangle – Understanding the formula for the area of a triangle, which is Area = 1/2 * base * height.
Effect of Changing Dimensions – Analyzing how changes in the base or height affect the overall area of the triangle.