Question

I will give Brainlyest!!

Answer 1

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!)