This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify the shape and given dimensions. The road sign is in the shape of a regular hexagon. The side length of the hexagon is s = 20 cm. Step 2: State the formula for the area of a regular hexagon. The area A of a regular hexagon with side length s is given by the formula: A = 3sqrt(3)2 s^2 Step 3: Substitute the given side length into the formula. Substitute s = 20 cm into the formula: A = 3sqrt(3)2 (20)^2 Step 4: Calculate the area. First, calculate 20^2: A = 3sqrt(3)2 (400) Multiply 3sqrt(3)2 by 400: A = 3sqrt(3) × (400)/(2) A = 3sqrt(3) × 200 A = 600sqrt(3) cm^2 To provide a numerical value, use sqrt(3) ≈ 1.732: A ≈ 600 × 1.732 A ≈ 1039.2 cm^2 The area of the road sign is approximately 1039.2 cm^2. 1039.2 cm^2 Send me the next one 📸