1. **Stating the problem:** We have a polygon composed of 7 squares arranged in a T-shape. Each square has side length $a$. The total area $A$ of the polygon is given as 288 m². We want to find the side length $a$ and the perimeter $U$ of the polygon. 2. **Formula for area of one square:** The area of one square is given by $$A_{\text{square}} = a^2$$ Since the polygon consists of 7 squares, the total area is $$A = 7 \times a^2$$ 3. **Calculate side length $a$:** Given $A = 288$ m², $$288 = 7 \times a^2$$ Divide both sides by 7: $$\frac{288}{7} = a^2$$ Using \cancel to show division: $$a^2 = \cancel{\frac{288}{7}}$$ Calculate the value: $$a^2 = 41.142857...$$ Take the square root of both sides: $$a = \sqrt{41.142857...}$$ $$a \approx 6.41 \text{ m}$$ 4. **Calculate perimeter $U$:** The perimeter is the sum of all outer sides. Since the polygon is made of 7 squares arranged in a T-shape, the perimeter is not simply $7 \times a$. We count the outer edges: - The horizontal line has 5 squares, so top side length is $5a$. - The vertical stem has 3 squares (1 bottom + 1 left + 1 right), so vertical sides add $3a$ each side. Perimeter formula: $$U = 2 \times (5a + 3a) = 2 \times 8a = 16a$$ Calculate $U$: $$U = 16 \times 6.41 = 102.56 \text{ m}$$ **Final answers:** - Side length $a \approx 6.41$ m - Perimeter $U \approx 102.56$ m