What is the answer??

HK = 20

Step-by-step explanation:

LM = (1/2) HK          {Mid point theorem}

2*(10x - 90) = 10x - 80

2*10x - 2*90 = 10x - 80

20x - 180     = 10x - 80                   {add 180 to both sides}

           20x  = 10x - 80 + 180

          20x  = 10x +100              {Subtract 10x from both sides from }

     20x -10x = 100

            10x  = 100

                x = 100/10

               x = 10

HK = 10x - 80

     = 10*10 - 80

     = 100 - 80

     = 20

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

the two may have that, even a breakdown is probably offered