Green Area of Square 20: 44 square units Green Area of Square 21: 45 square units Explanation: See solution
Practice makes perfect
Let's begin by counting the green blocks in each of the given squares.
Square
Number of Green Blocks
1
5
2
8
3
9
4
12
5
13
Now let's try to find the pattern. First we will take a look at odd numbered squares. We can see that the number of green blocks is equal to the number of the square multiplied by 2 and increased by 3.
Square Number
Rule
Number of Green Blocks
1
2* 1+ 3
5
3
2* 3+ 3
9
5
2* 5+ 3
13
Next, let's focus on even numbered squares. This time the number of green blocks is equal to the number of the square multiplied by 2 and increased by 4.
Square Number
Rule
Number of Green Blocks
2
2* 2+ 4
8
4
2* 4+ 4
12
Let's summarize our findings. Let x represent the number of the square and y represent the number of green blocks.
& y=2x+3 ifxis an odd number
& y=2x+4 ifxis an even number
Now we can find the number of green blocks in Square 20. We will use the second formula because 20 is an even number.
There are 44 green blocks in Square 20. Because each block has an area of one square unit, this means that the green area of Square 20 is 44 square units. Next, let's evaluate the number of green blocks in Square 21. This time we will use the first formula since 21 is an odd number.
