Answer:
The area of the 40th figure is 1,682
Step-by-step explanation:
Notice that the area of each figure is the area of the rectangle with an addition of two (2).
For example.
Figure 5:
Area = (8 * 5) + 2 = 40 + 2 = 42
There is always an increase in length and width for every successive figure.
Figure 6 would be:
(9 * 6) + 2 = 56
Now, we have
Area = n(n+2) + 2
For n = 2
2(2+2) + 2 = 10
n = 3
3(3+2) + 2 = 17
n = 4
4(4+2) + 2 = 26
n = 5
5(5+2) + 2 = 37
n = 6
6(6+2) + 2 = 50
Therefore, for the 40th figure, the area is:
n = 40
40(40+2) + 2 = 1,682