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Need to find the area for the 40th figure given the info provided

Need to find the area for the 40th figure given the info provided-example-1
User YanDatsiuk
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1 Answer

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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

User Boluc Papuccuoglu
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