There are a couple of ways you can find the area of G to be 18 small squares:
1) Consider G to be a trapezoid with bases 10√2 and 8√2 and height √2. Then its area is
A = (1/2)(b1 +b2)h
A = (1/2)(10√2 +8√2)√2 = 18
2) Consider G to be a parallelogram of base 2 and height 8, topped with an isosceles right triangle of side lengths 2. Then the area is
A = bh . . . . for the parallelogram
= 2·8 = 16
and
A = (1/2)bh . . . . for the triangle
= (1/2)2·2 = 2
for a totoal of
A = 16 + 2 = 18.
Of course the area of the large square is 10·10 = 100 small squares.
If darts land randomly within the border of the large square, the probability of landing in area G is 18/100 = 0.18.
