The formula $A = \frac{1}{2}bh$ represents the area $A$ of a triangle, where:

• $b$ is the length of the base of the triangle.
• $h$ is the height of the triangle, which is the perpendicular distance from the base to the opposite vertex.

How the Formula Works

1. Base (b): This is one side of the triangle that is chosen as the reference base.
2. Height (h): This is the perpendicular distance from the base to the opposite vertex of the triangle.

The formula effectively calculates the area by considering half the product of the base and height. This works because any triangle can be considered half of a rectangle if we draw a height that splits the rectangle into two equal triangles.

Example Calculation

Suppose you have a triangle with a base $b = 8$ units and a height $h = 5$ units:

$A = \frac{1}{2} \times b \times h = \frac{1}{2} \times 8 \times 5 = \frac{1}{2} \times 40 = 20 \, \text{square units}$

Would you like more details, or do you have any questions?

Here are five questions to explore further:

1. How do you derive the area formula for a triangle?
2. What happens to the area if both base and height are doubled?
3. How do you find the height of a triangle if the area and base are known?
4. Can this formula be used for all types of triangles (e.g., right, obtuse)?
5. How do you calculate the area of a triangle with vertices given on a coordinate plane?

Tip: Always make sure the height is perpendicular to the chosen base for an accurate area calculation.