Question

The base of a triangle is doubled and the height remains the same. Explain how the area changes. Use examples.

Answer 1

[AI-generated answer — Bot]

The area of a triangle is calculated by multiplying the base by the height and then dividing by 2. Therefore, when the base is doubled and the height remains the same, the area of the triangle will also double.

For example, if the base of the triangle is 4 and the height is 3, the area would be 6. If the base is doubled to 8, the area would be 12.

Answer 2

[AI-generated answer — Explain Bot]

To determine how the area of a triangle changes when the base is doubled while the height remains the same, we can use the formula for the area of a triangle: A = (1/2) * base * height.

Let's consider an example to illustrate this concept. Suppose we have a triangle with a base of 4 units and a height of 6 units. Using the area formula, we can calculate the area as A = (1/2) * 4 * 6 = 12 square units.

Now, let's double the base to 8 units while keeping the height the same at 6 units. Using the area formula again, we find that the new area is A = (1/2) * 8 * 6 = 24 square units.

Comparing the original area of 12 square units with the new area of 24 square units, we see that doubling the base results in a doubling of the area as well.

In general, when the base of a triangle is doubled while the height remains the same, the area of the triangle also doubles. This can be explained by understanding that the area of a triangle is directly proportional to its base.

Answer 3

[AI-generated answer — Step-by-Step Bot]

When the base of a triangle is doubled while the height remains the same, the area of the triangle also doubles. This is because the area of a triangle is calculated using the formula:

Area = (1/2) * base * height

Let's consider an example to understand this better:

Example:
Let's say we have a triangle with a base of 4 units and a height of 3 units. Using the area formula, we can calculate the original area:

Original Area = (1/2) * base * height
= (1/2) * 4 * 3
= 6 square units

Now, if we double the base to 8 units while keeping the height unchanged at 3 units, we can calculate the new area:

New Area = (1/2) * doubled base * height
= (1/2) * 8 * 3
= 12 square units

As you can see, the new area of the triangle is double the original area. This is because increasing the base while keeping the height the same effectively increases the overall area of the triangle.