Final answer:
To find the area of the circumscribed regular hexagon with a 2-meter radius, you calculate the area of 6 equilateral triangles and approximate the final area to 10 m², rounded to two significant figures because the radius is given to two significant figures.
Step-by-step explanation:
The question asks to obtain the area of a circumscribed regular hexagon with a radius of 2 meters. To find the area of a regular hexagon, you can calculate the area of the 6 equilateral triangles that make up the hexagon. Since the radius of the circumscribed circle is given as 2 meters, each side of the regular hexagon will also be 2 meters (radius equals side length in a circumscribed hexagon).
The area of each equilateral triangle can be calculated using the formula: A = (\sqrt{3}/4) × side². So, the area of one triangle is (\sqrt{3}/4) × (2 m)² = (\sqrt{3}/4) × 4 m² = \sqrt{3} m². Since there are 6 such triangles in the hexagon, the total area would be: 6 × \sqrt{3} m².
Using this calculation, we can approximate the value of \sqrt{3} as roughly 1.732. Hence the area of the hexagon is 6 × 1.732 m² = 10.392 m². This area should then be rounded to two significant figures because the radius is given to two significant figures, resulting in 10 m².