What is the area of rectangle defg shown below.

  60 square units

Step-by-step explanation:

You can get there a couple of ways.

One way is to consider the enclosing rectangle, which is 9 units by 11 units, so has an area of 99 square units. From that will be subtracted two triangles having height 2 and width 6, and two triangles having height 3 and width 9. Thus the net area in rectangle DEFG is ...

  99 - 2·6 - 3·9 = 60 . . . square units

__

Another way is to find the lengths of each of the sides and multiply those.

  Short side = √(2²+6²) = 2√10

  Long side = √(3²+9²) = 3√10

area = short side × long side = (2√10)(3√10) = 6·10 = 60 . . . square units

Let  be the first integer. the next integer must then be  .the difference of their squares is an odd integer, so    is expandable.      therefore    all even  integers  are divisible by 2. forces  to always be an even integer. it forces 2 to be a factor of  .if you add 1 to any even integer, you get an odd integer.so 2n makes always  an even integers ; adding 1 therefore makes it always odd.