The diagram below shows a rectangle inside a regular hexagon

The diagram below shows a rectangle inside a regular hexagon. The apothem of the hexagon is 17.32 units. To the nearest square unit, what is the area of the shaded region? Apothem length: 17.32 719 square units 373 square units 1039 square units 1359 square units

Solution

The correct option is A.719 sq units

Area of hexagon =6 times Area of equilateral triangle=6 x 1/2 X 20 x 17.32=1039.2sq units

Area of rectangle given =20X16=320 sq units

Area of Shaded region = Area of Hexagon - Area Rectangle

                                 = 1039.20 - 320

                                 = 719.20sq units