The problem is written in Danish and translates to the following:

Task 622:
In triangle $\triangle ABC$, $c = 8.2$ (base of the triangle), and $h = 2.9$ (height from $C$). Draw a sketch of the triangle and calculate its area.

Solution:

The area $A$ of a triangle can be calculated using the formula: $A = \frac{1}{2} \cdot \text{base} \cdot \text{height}.$

Here:

• Base ($c$) = $8.2$
• Height ($h$) = $2.9$

Plugging the values into the formula: $A = \frac{1}{2} \cdot 8.2 \cdot 2.9.$

Calculation: $A = \frac{1}{2} \cdot 23.78 = 11.89.$

Thus, the area of the triangle is: $\boxed{11.89 \, \text{cm}^2.}$

Sketch:

The sketch involves:

1. Drawing a triangle $\triangle ABC$, where:
   • $AB = c = 8.2$ (base).
   • $h = 2.9$ is the perpendicular height from vertex $C$ to base $AB$.
2. Labeling the dimensions accordingly.

Would you like me to generate a digital sketch of the triangle for you?

Do you have further questions, or would you like additional details?

Here are five related questions to expand your understanding:

1. How do you derive the formula for the area of a triangle?
2. What happens to the area if both the base and the height are doubled?
3. How would you calculate the area if only the angles and side lengths are given?
4. Can you calculate the area of an equilateral triangle with side length $a$ using only geometry?
5. How does the height relate to the angles in a triangle?

Tip: Always confirm that the height you use is perpendicular to the chosen base when calculating the area of a triangle.