1. Let's identify the elements and properties of the kite from the given information. 2. The kite has two pairs of equal sides: the top pair each labeled $a$, and the other sides are implied equal by symmetry. 3. The vertical diagonal is labeled $2a$, and the horizontal diagonal is given as $2$ cm ("o 2 ס"מ" means approximately 2 cm). 4. There is a right angle between the diagonals, indicated by the small square at their intersection. This means the diagonals are perpendicular. 5. Since the diagonals are perpendicular and they intersect inside the kite, the diagonals bisect each other. So, half of the vertical diagonal is $a$, and half of the horizontal diagonal is $1$ cm. 6. We want to find the length of side $a$ or any other related measurement. Using the right triangle formed by half the diagonals: $$\text{side } a = \sqrt{a^2 + 1^2}$$ However, this equation is inconsistent as written; we need to clarify the sides. 7. Actually, the kite's side $a$ corresponds to the hypotenuse of the right triangle formed by half the diagonals: the two legs are half diagonals $a$ (vertical) and $1$ (horizontal). 8. Apply the Pythagorean theorem to find $a$: $$a = \sqrt{a^2 + 1^2}$$ This implies $a^2 = a^2 + 1$, which is a contradiction. 9. Instead, the correct method is: Since half the vertical diagonal is $a$, and half the horizontal diagonal is $1$, then side $a$ (the kite's side) is the hypotenuse: $$a = \sqrt{a^2 + 1^2}$$ This is circular; solve for $a$ carefully. 10. Let $s$ be the side length $a$. Then by Pythagoras on the half-diagonal right triangle: $$s = \sqrt{a^2 + 1^2}$$ But $a$ is both side length and half vertical diagonal; this is confusing. 11. Let me denote: - $d_v = 2a$ (vertical diagonal) - So half vertical diagonal is $a$ - $d_h = 2$ cm (horizontal diagonal), half is $1$ 12. Then the kite's side $s$ is: $$s = \sqrt{a^2 + 1^2}$$ 13. Given the kite, side length $s$ equals $a$ (top side label), so: $$a = \sqrt{a^2 + 1^2}$$ 14. Square both sides: $$a^2 = a^2 + 1$$ 15. Subtract $a^2$ both sides: $$0 = 1$$ 16. Contradiction means labeling is mixed. 17. Possibly $a$ on sides and half vertical diagonal are different variables; let's rename variables: - Let side length = $x$ - Half vertical diagonal = $a$ 18. Then, $$x = \sqrt{a^2 + 1^2} = \sqrt{a^2 + 1}$$ 19. Without numerical values for $a$, the problem cannot be solved numerically. 20. Therefore, the side length $x$ in terms of $a$ is: $$x = \sqrt{a^2 + 1}$$ Summary: - The kite has vertically vertical diagonal $2a$ cm. - The horizontal diagonal is 2 cm. - Diagonals are perpendicular. - Side length $x = \sqrt{a^2 + 1}$ cm. No numerical answer unless $a$ is given.