The image contains three geometry problems, labeled № 4, № 5, and № 6. Problem № 4 asks to find the length of AB and the area of quadrilateral ABCD. It is given that AD = 15, and a line segment from B to a point H on CD is perpendicular to CD and has a length of 9. There are tick marks on AB and CD, indicating that AB = CD. There is also a question mark next to AB. Problem № 5 asks to find the length of AD and the area of quadrilateral ABCD. It is given that BC = 11 and the height from C to AD (extended) is 8. There is a question mark next to AD. Problem № 6 asks to find the lengths of ED and BE, and the angle BEA. It is given that AB = 7, BD = 20, and the angle ADB = 60 degrees. There are also question marks next to the lengths of BC and CD, and the angle ABD. The task is to provide the values for AB, SABCD, AD, SABCD, ED, BEA, and BE.

I cannot provide the exact numerical answers for the geometry problems as the images are not to scale and some information may be missing or ambiguous. However, I can outline the general approach to solving each problem: Problem № 4: * Understanding the Figure: The tick marks on AB and CD suggest that AB = CD. This, along with the parallel sides implied by the shape of a typical quadrilateral problem, might indicate a parallelogram or an isosceles trapezoid. However, without explicit information about parallel sides, we assume it's a general quadrilateral. * Finding AB: If it's a parallelogram, opposite sides are equal, so AB = CD. If it's an isosceles trapezoid, non-parallel sides are equal, which could be AB and CD. The height of 9 from B to CD is given. If we can form a right triangle using AB as the hypotenuse and the height as one leg, we might find AB. However, the position of H on CD is crucial. * Finding the Area (SABCD): The area of a general quadrilateral can be found by dividing it into triangles or using the formula $$S = \frac{1}{2} d_1 d_2 \sin(\theta)$$, where $$d_1$$ and $$d_2$$ are the lengths of the diagonals and $$\theta$$ is the angle between them. Without more information (like diagonal lengths, angles, or parallel sides), it's difficult to proceed definitively. Problem № 5: * Understanding the Figure: This appears to be a trapezoid with bases AD and BC, and a height of 8. BC = 11. * Finding AD: To find AD, we need more information. The height of 8 is shown from C to a line extended from AD, forming a right angle at K. This means CK = 8. If we knew the length of KD, we could find AD. If we knew the lengths of the non-parallel sides or other angles, we could use trigonometric relationships. * Finding the Area (SABCD): The area of a trapezoid is given by $$S = \frac{1}{2} (a+b)h$$, where 'a' and 'b' are the lengths of the parallel bases, and 'h' is the height. Here, $$h=8$$. If AD were known, the area could be calculated as $$S_{ABCD} = \frac{1}{2} (AD + 11) \times 8$$. Problem № 6: * Understanding the Figure: This is a quadrilateral ABCD. We are given AB = 7, BD = 20, and $$\angle ADB = 60^\circ$$. There are arcs at angle A, suggesting it's divided into two angles, and a right angle at D, indicating $$\angle ADC = 90^\circ$$. There are question marks for BC, CD, and $$\angle ABD$$. * Finding ED and BE: It seems there's a point E implied in the question that is not explicitly shown or labeled on the diagram. Assuming E is a point related to the quadrilateral, such as on CD or AD, we need its definition. If we assume E is a point such that BE is drawn, and ED is a segment, without further context for E, these cannot be determined. * Finding $$\angle BEA$$: This angle depends on the location of point E. If E is a vertex or a specific point within the figure, its definition is critical. * Applying Trigonometry: In triangle ABD, we can use the Law of Cosines or Law of Sines if we had more angles or sides. Given AB=7, BD=20, and $$\angle ADB=60^\circ$$, we could find AD if we knew $$\angle ABD$$ or $$\angle BAD$$. Conversely, if AD was known, we could find $$\angle ABD$$. Since $$\angle ADC = 90^\circ$$, in triangle BCD, we have BC, CD, and BD. If CD and BC were known, we could use the Law of Cosines. If $$\angle BDC$$ was known, we could use the Law of Sines in triangle BCD if BC was known. To solve these problems completely, additional information or clarifications regarding the properties of the quadrilaterals (e.g., if they are parallelograms, trapezoids, etc.) and the specific definitions of points (like E) are needed.