Final answer:
The area of a polygon inscribed in a circle can be calculated using the formula A = ½ n r² ² multiplied by the number of sides and the appropriate significant figures from the radius measurement.
Step-by-step explanation:
To calculate the area of a polygon inscribed in a circle, one must understand the relationship between the circle and the inscribed polygon. The perimeter of the polygon is less than the circumference of the circle, and the area of the polygon is less than the area of the circle. Therefore, an inscribed polygon can be approached by dividing it into triangles. The area of these triangles can be calculated using trigonometric methods or by dividing the polygon into a number of equal triangles that meet at the center of the circle. Once the area of one triangle is known, it can be multiplied by the number of triangles to get the total area of the polygon.
Using a calculator, one can use the formula A = ½ n r² ², where n is the number of sides, r is the radius of the circle, and ² is the angle in radians of the central angle corresponding to one of the triangles. It is essential to ensure the proper use of units and significant figures. The calculator's precision needs to match the number of significant figures in the measurement with the least number of significant figures to maintain accuracy in the final result.
For example, if we know the radius of the circle and the number of sides of the polygon, we can easily determine the central angle for one of the triangles by dividing 360 by the number of sides. Then, we can calculate the area of a triangle and multiply by the number of sides to get the total area of the polygon. If measurements are in meters, our final area will be in square meters. Considering significant figures, if our measurements are precise up to two decimal places, our final answer should also be rounded off to two significant figures.