A company produces wooden signs shaped like regular octagons of side 20 cm. If wood costs ₹5/cm² and design costs ₹200 per piece, what is the total cost per sign?
Show answer & explanation
Correct answer: A
Explanation
Area of a regular octagon = 2(1 + √2) × side²
= 2(1 + √2) × 20²
= 2(1 + √2) × 400
= 800(1 + √2) sq cm
Cost of wood = 5 × 800(1 + √2)
= 4000(1 + √2)
≈ ₹9656.85
Cost of design = ₹200
Therefore, total cost per sign = 9656.85 + 200
= ₹9856.85 (approx.)