How do you find the area of a triangle?

Definition

The area of a triangle is the amount of space enclosed by its three sides. For a triangle with base $b$ and height $h$, the area $A$ is given by:

$$ A = \frac{1}{2} b h $$

• The base ($b$) can be any side of the triangle.
• The height ($h$) is the perpendicular distance from the chosen base to the opposite vertex.

Worked Example

Problem:
Find the area of a triangle with base $b = 8$ units and height $h = 5$ units.

Step 1: Write the formula:

$$ A = \frac{1}{2} b h $$

Step 2: Substitute the given values:

$$ A = \frac{1}{2} \times 8 \times 5 $$

Step 3: Calculate:

$$ A = \frac{1}{2} \times 40 = 20 $$

Final Answer:
The area of the triangle is $20$ square units. ## Takeaways - The area formula for a triangle is $A = frac{1}{2} b h$.

• Always use the perpendicular height corresponding to the chosen base.
• This formula applies to all triangles, regardless of type.