1. The problem describes a kite-shaped quadrilateral with perpendicular diagonals. 2. The diagonals are divided into segments: one diagonal has segments 6 cm and 4 cm, so its total length is $$6 + 4 = 10$$ cm. 3. The other diagonal has a segment of 3 cm, and since diagonals of a kite are perpendicular and bisect each other, the other segment is also 3 cm, so total length is $$3 + 3 = 6$$ cm. 4. The area of a kite is given by $$\text{Area} = \frac{1}{2} \times d_1 \times d_2$$, where $$d_1$$ and $$d_2$$ are the lengths of the diagonals. 5. Substitute the values: $$\text{Area} = \frac{1}{2} \times 10 \times 6 = 30$$ cm². 6. The perimeter (scope) is the sum of all sides. The kite has two pairs of equal adjacent sides: one pair is 6 cm and 4 cm, the other pair corresponds to the sides facing the 3 cm diagonal segments, which requires calculation. 7. Using the right triangle formed by half diagonals (6 cm and 3 cm): side length = $$\sqrt{6^2 + 3^2} = \sqrt{36 + 9} = \sqrt{45} = 3\sqrt{5} \approx 6.71$$ cm. 8. Similarly, triangle with the other half diagonal 4 cm and 3 cm: side length = $$\sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5$$ cm. 9. Perimeter = $$2 \times (6.71 + 5) = 2 \times 11.71 = 23.42$$ cm approximate. Final answers: - Area: 30 cm² - Perimeter: approximately 23.42 cm