Percentage decrease in the area of a triangle when the sides are reduced to half

To find the percentage decrease in the area of a triangle when the sides are reduced to half, we need to consider the relationship between the sides and the area of a triangle.

1. Understanding the relationship between sides and area of a triangle:
The area of a triangle is given by the formula A = (1/2) * base * height, where the base and height are perpendicular to each other. The base and height are usually the two sides of the triangle that form a right angle.

2. Reducing the sides to half:
When the sides of a triangle are reduced to half, it means that each side is halved in length. So, if the original sides of the triangle were 'a', 'b', and 'c', the new sides would be 'a/2', 'b/2', and 'c/2'.

3. Calculating the new area of the triangle:
To calculate the new area of the triangle, we need to use the formula A = (1/2) * base * height. Since the base and height are halved, the new area can be calculated as A' = (1/2) * (a/2) * (b/2). Simplifying this expression gives A' = (1/4) * a * b.

4. Finding the percentage decrease:
To find the percentage decrease in the area, we need to compare the original area (A) with the new area (A') and calculate the difference as a percentage of the original area.

The percentage decrease can be calculated using the formula: Percentage Decrease = ((A - A') / A) * 100.

Substituting the values, we get: Percentage Decrease = ((A - (1/4) * a * b) / A) * 100.

5. Example:
Let's consider an example to illustrate this calculation. Suppose we have a triangle with sides of length 6, 8, and 10 units.

The original area of the triangle can be calculated using the formula: A = (1/2) * 6 * 8 = 24 square units.

When the sides are reduced to half, the new sides become 3, 4, and 5 units.

The new area of the triangle can be calculated using the formula: A' = (1/4) * 6 * 8 = 12 square units.

Substituting these values into the percentage decrease formula, we get: Percentage Decrease = ((24 - 12) / 24) * 100 = 50%.

Therefore, the percentage decrease in the area of the triangle when the sides are reduced to half is 50%.