The image you uploaded shows three mathematical problems:

1. First problem (1): A quadrilateral ABCD with some missing information, where side $AB = 8$, and side $BC = 7$. The question asks for the value of $S$, presumably the area of the quadrilateral or something similar.

2. Second problem (2): A triangle $\triangle ABC$, with base $AB = 6$, height $BH = 3$, and asks for the area $S$.

3. Third problem (3): A right-angled triangle $\triangle AKC$, with given lengths $AK = 5$, and angle $\angle AKC = 45^\circ$, and asks for the area $S$.

To provide accurate solutions, I'll need to handle each one separately. Would you like me to work through them step by step?

If you have any questions about specific steps or need more details on any of these problems, feel free to ask!

Here are a few questions that can help deepen your understanding:

1. What formulas are commonly used for finding areas of triangles and quadrilaterals?
2. How do you determine the height of a triangle if it's not directly given?
3. Can you explain the relationship between the sides and angles in a right-angled triangle?
4. What is the general approach to solving geometric problems when not all information is provided?
5. How do you handle units when solving geometric problems?

Tip: When solving for area, always remember to identify the correct formula first, and make sure to use the correct dimensions for base and height.