1. **Problem Statement:** Calculate the perimeter and height $h$ of the bottom-center polygon, which consists of a trapezoid with a base of 15 cm, two right triangles on top with sides 7 cm, and segments of 6 cm each on the base. 2. **Given:** - Base length $= 15$ cm - Two segments on the base: $6$ cm and $6$ cm (left and middle parts) - Right triangle side length $= 7$ cm - Height of trapezoid $= h$ - Right angles at the base corners 3. **Find $h$ using the Pythagorean theorem:** Each right triangle has a base segment of $6$ cm and hypotenuse $7$ cm. Using Pythagoras: $$7^2 = 6^2 + h^2$$ $$49 = 36 + h^2$$ $$h^2 = 49 - 36 = 13$$ $$h = \sqrt{13}$$ cm 4. **Calculate the perimeter:** The polygon has the following sides: - Bottom base: $15$ cm - Two vertical sides: left side $h = \sqrt{13}$ cm, right side $13$ cm (given) - Two slant sides (hypotenuses of triangles): each $7$ cm - The top middle segment: $6$ cm Sum all sides: $$P = 15 + \sqrt{13} + 13 + 7 + 7 + 6$$ $$P = 15 + 3.6055 + 13 + 7 + 7 + 6 = 51.6055$$ cm 5. **Final answers:** - Height $h = \sqrt{13} \approx 3.61$ cm - Perimeter $P \approx 51.61$ cm