The formula involving "bh" is most commonly associated with calculating the area of a triangle. However, the reference provided discusses how to manipulate the formula A = (1/2)bh to solve for the height h. Let's break down both aspects:
The Area of a Triangle Formula
The formula for the area of a triangle is:
-
A = (1/2)bh
Where:
- A represents the area of the triangle.
- b represents the length of the base of the triangle.
- h represents the height of the triangle, which is the perpendicular distance from the base to the opposite vertex.
This formula means that the area of a triangle is equal to one-half the product of its base and height.
Solving for Height (h)
The provided video demonstrates how to solve for height in the area of a triangle formula:
- Start with the formula: A = (1/2)bh
- Multiply both sides by 2: This action eliminates the fraction.
- 2 A = 2 (1/2)bh
- 2A = bh
- Divide both sides by b: To isolate h, divide each side of the equation by b.
- 2A / b = bh / b
- 2A / b = h
Therefore, the formula to calculate the height of a triangle when the area and the base are known is:
- h = 2A / b
Examples
-
Example 1: If the area of a triangle is 20 square units and its base is 10 units, you can use the formula to calculate the height:
- h = (2 * 20) / 10
- h = 40 / 10
- h = 4 units
-
Example 2: If you know the height (h) and the base (b) you can compute the area. Let's say that the height is 5 and the base is 6:
- A = (1/2) 6 5
- A = 15
Summary of Key Formulas
| Formula | Purpose |
|---|---|
| A = (1/2)bh | Calculates the area of a triangle |
| h = 2A / b | Calculates the height of a triangle |
In short, "bh" is part of the fundamental formula used to determine the area of a triangle, and by manipulating it, we can solve for the height (h), when needed.
