Answer:
66.91 km^2
Step-by-step explanation:
This answer will be long:
Interior angles of hexagon sum to (4)(180) = 720 each is 120 degrees
each side is 24/6 = 4 km
area of hexagon = 12 * 1/2 2 * (2 tan60) = 41.5692 km ^2
L triangle 5 = hypot leg1 = 4 leg2 = 3 area = 1/2 * 3 * 4 = 6 km^2
TOP triangle is 4 = hypot leg1 = 3.464 leg2 = 2
area = 1/2 * 3.464 * 2 = 3.464 km^2
R triangle two legs = 4 area = 1/2 * 4 x 4 = 8 km^2
BOTTOM triangle two sides = 4 use sin rule sin40/4 = sin 100/x
third side = 4/sin 40 * sin 100 = 6.1284 km
semi perimter = ( 4 + 4 + 6.1284) / 2 = 7.0641 km
Use Herron's rule for area =
sqrt ( 7.0641 (7.0641-4)(7.0641-4)(7.0641-6.1284) ) = 7.878 km^2
add all of the areas to get 66.91 km^2 (IF I made no math errors!)
