A typical stop sign is in the shape of a regular octagon. The length of a side of a stop sign is 38.7 centimeters, and the radius is 50.6 centimeters. Calculate the area of the stop sign to the nearest square centimeter.

The area of the octagon stop sign to the nearest square centimetres is 187 cm²

Step-by-step explanation:

The stop sign is in the shape of a regular octagon, therefore, the area is given by the following relation;

Area of regular octagon = 2 × (Side Length)² × (1 + √2)

Where:

Side Length = 38.7 cm

Area of regular octagon = 2 × 38.7 × (1 + √2) = 186.86 cm²

The area of the octagon stop sign = 186.86 cm²

The area of the octagon stop sign to the nearest square centimetres = 187 cm².