Question

help asap pls. 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

we know that
area of the shaded region=area of a regular  hexagon-area of the rectangle

find the area of the rectangle
Area rectangle=18*21------> 378 units²

find the area of a regular hexagon
area of regular hexagon=n*L*apothem/2
where
n is the number of sides------> n=6
L is the long side of the hexagon-----> L=18 units
apothem=15.59 units
area of regular hexagon=6*18*15.59/2-----> 841.86 units²

area of the shaded region=841.86-378------> 463.86-----> 464 units²

the answer is
464 units²