Question

1. what is the area of this shape?

□ = 1 square unit

Explanation:

Step1: Count squares row by row

First row (top): 1 square.
Second row: 4 squares.
Third row: 4 squares.
Fourth row: 4 squares.
Fifth row: 2 squares.
Sixth row: 2 squares. Wait, no, let's re - count properly. Wait, looking at the figure:

Topmost square: 1.

Then the next part:

Row 1 (below top): 4 squares.

Row 2: 4 squares.

Row 3: 4 squares.

Row 4: 2 squares.

Row 5: 2 squares. Wait, no, maybe a better way: Let's list each row's square count:

• Top row: 1 square.
• Row 2 (under top): 4 squares.
• Row 3: 4 squares.
• Row 4: 4 squares.
• Row 5: 2 squares.
• Row 6: 2 squares. Wait, no, that's wrong. Wait, let's look again. The figure:

Top: 1 square.

Then a 4 - column, 3 - row block? Wait, no, let's count each square:

First, the top square: 1.

Then the next part:

First horizontal line (after top): 4 squares.

Second horizontal line: 4 squares.

Third horizontal line: 4 squares.

Fourth horizontal line: 2 squares.

Fifth horizontal line: 2 squares. Wait, no, maybe I made a mistake. Let's count one by one:

Top square: 1.

Then, the next rows:

Row 1 (y - axis, below top): 4 squares (columns 1 - 4).

Row 2: 4 squares (columns 1 - 4).

Row 3: 4 squares (columns 1 - 4).

Row 4: 2 squares (columns 1 - 2).

Row 5: 2 squares (columns 1 - 2).

Wait, no, that can't be. Wait, maybe the correct count is:

Top: 1.

Then, the main block:

From row 2 to row 4 (3 rows) with 4 columns: 3×4 = 12.

Then row 5 and row 6 with 2 columns: 2×2 = 4.

Plus the top 1: 1+12 + 4=17? Wait, no, let's count again.

Wait, let's draw mentally:

• Square at (1,4) (top right): 1.

Then, the rectangle below it:

Columns 1 - 4, rows 2 - 4: that's 3 rows ×4 columns = 12.

Then, columns 1 - 2, rows 5 - 6: 2 rows ×2 columns = 4.

Total: 1+12 + 4=17? Wait, no, maybe I messed up the rows. Wait, let's count each square:

1 (top) + 4 (row 2) + 4 (row 3) + 4 (row 4) + 2 (row 5) + 2 (row 6)=1+4 + 4+4+2+2 = 17? Wait, no, 1+4 is 5, +4 is 9, +4 is 13, +2 is 15, +2 is 17. Wait, but maybe another way: Let's count all squares:

Top: 1.

Then, the 4 - column, 3 - row (rows 2 - 4): 3×4 = 12.

Then, 2 - column, 2 - row (rows 5 - 6): 2×2 = 4.

1+12 + 4 = 17. Wait, but maybe I made a mistake. Wait, let's count again:

Top square: 1.

Row 2 (below top): 4 squares (left to right: 4).

Row 3: 4 squares.

Row 4: 4 squares.

Row 5: 2 squares.

Row 6: 2 squares.

1+4+4+4+2+2 = 17.

Wait, but let's check again. Alternatively, maybe the correct count is 1 + 4×3+2×2=1 + 12 + 4 = 17.

Wait, but maybe I miscounted. Wait, let's see:

Another approach: Each small square is 1 unit. So we can count the number of small squares.

Looking at the figure:

• 1 square at the top.

• Then, a 4 - column, 3 - row grid: 3×4 = 12.

• Then, a 2 - column, 2 - row grid: 2×2 = 4.

Total: 1+12 + 4 = 17.

Wait, but let's count again:

Top: 1.

Row 2: 4.

Row 3: 4.

Row 4: 4.

Row 5: 2.

Row 6: 2.

1+4=5; 5+4=9; 9+4=13; 13+2=15; 15+2=17. Yes, so total 17 square units.

Step2: Sum the counts

We have 1 (top) + 4 (row2) + 4 (row3) + 4 (row4) + 2 (row5) + 2 (row6) = 17.

Answer:

17 square units