To find the area of triangle $ABC$, we can use the formula for the area of a triangle:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

In this triangle:

• The base $BC = 8$ cm.
• The height from $A$ to line $BC$ is given as $10$ cm.

Substitute these values into the area formula:

$\text{Area} = \frac{1}{2} \times 8 \times 10 = \frac{1}{2} \times 80 = 40 \text{ square centimeters}$

Thus, the area of triangle $ABC$ is $40$ cm².

Would you like further details or have any other questions?

Here are some related questions you might explore:

1. How would the area change if the height were different?
2. What other methods could be used to find the area of a triangle?
3. How does this area formula apply to non-right triangles?
4. Can you find the area of a triangle if only the side lengths are known?
5. How would you find the perimeter of triangle $ABC$?

Tip: Always ensure the height is perpendicular to the base when calculating the area of a triangle.