The diagram below shows a rectangle inside a regular hexagon the apothem of the hexagon is 15.59 units to the nearest square unit what is the area of the shaded region?

Answer 1

To find the area of the shaded region (the rectangle inside the hexagon), we first calculate the area of the hexagon using the formula ( \text{Area} = \frac{3\sqrt{3}}{2} \times a^2 ), where ( a ) is the apothem. Given that the apothem is 15.59 units, the area of the hexagon is approximately ( \frac{3\sqrt{3}}{2} \times (15.59^2) \approx 609.67 ) square units. Assuming the rectangle’s area is not specified, the shaded area would be the hexagon's area minus the rectangle's area. If the rectangle's area is provided, subtract it from the hexagon's area to find the shaded region's area.