Question

find the area of the shaded shape. 1 unit 1 unit square units

Explanation:

Step1: Count full squares

Looking at the shaded shape, we can split it or count the number of 1x1 square units. Let's count row by row. The top row (first row of the shaded part) has 5 squares. Then the next rows: let's see the columns. Alternatively, we can think of the shape as a combination. Wait, actually, let's count each square:

First, the left - most part: the top horizontal part has 2 squares (wait, no, let's do it properly. Let's count the number of unit squares.

Looking at the grid, each square is 1 unit by 1 unit, so area 1 square unit.

Let's count the shaded squares:

Row 1 (top shaded row): 5 squares (columns 3 - 7, assuming columns start from 1).

Row 2: 3 squares? Wait, no, maybe a better way: the shape can be considered as a large rectangle minus a smaller rectangle, but maybe counting is easier.

Wait, let's count:

Looking at the figure, the shaded region:

- The top horizontal strip: length 5, height 1: 5*1 = 5.

- Then the vertical strip on the right: from row 2 to row 6 (assuming row 1 is top), and columns 5 - 7. Wait, no, let's count the number of squares:

Let's list the coordinates (row, column) of each shaded square.

Row 1 (top row of shaded): columns 3,4,5,6,7 → 5 squares.

Row 2: columns 5,6,7 → 3 squares.

Row 3: columns 5,6,7 → 3 squares.

Row 4: columns 5,6,7 → 3 squares.

Row 5: columns 5,6,7 → 3 squares.

Row 6: columns 5,6,7 → 3 squares. Wait, that can't be right. Wait, no, maybe I messed up the rows.

Wait, looking at the grid, the shaded shape: the top part is a horizontal rectangle (length 5, height 1) and then a vertical rectangle (length 3, height 5)? Wait, no, let's count the number of squares:

Wait, another approach: the total number of shaded squares. Let's count:

First, the top row (the first horizontal part) has 5 squares (since from column 3 to column 7, 5 columns, 1 row).

Then, the part below it: from row 2 to row 6 (that's 5 rows) and from column 5 to column 7 (3 columns). So 5*3 = 15? Wait, no, 5 rows (row 2 to row 6 is 5 rows: 2,3,4,5,6) and 3 columns (5,6,7). Then 5*3 = 15, plus the top 5: 5 + 15 = 20? Wait, no, that's not correct. Wait, maybe I made a mistake in rows.

Wait, let's look at the figure again. The shaded shape: the top horizontal bar is 5 units long (5 squares) and 1 unit tall. Then the vertical bar on the right is 5 units tall (from row 2 to row 6, 5 rows) and 3 units wide (columns 5 - 7, 3 columns). But wait, the intersection of the top bar and the vertical bar is counted twice, so we need to use the principle of inclusion - exclusion. Wait, no, actually, the top bar is from row 1, columns 3 - 7 (5 squares). The vertical bar is from row 2 - 6, columns 5 - 7 (3 columns, 5 rows: 3*5 = 15). But the square at (row 1, column 5 - 7) is already counted in the top bar? No, the top bar is row 1, columns 3 - 7. The vertical bar is row 2 - 6, columns 5 - 7. So there is no overlap. Wait, row 1, columns 5 - 7 are part of the top bar, and row 2 - 6, columns 5 - 7 are part of the vertical bar. So total squares: 5 (row 1) + 3*5 (rows 2 - 6) = 5+15 = 20? Wait, no, 3*5 is 15, 5 + 15 = 20? Wait, but let's count manually:

Row 1 (top): 5 squares (columns 3,4,5,6,7) → 5.

Row 2: columns 5,6,7 → 3.

Row 3: columns 5,6,7 → 3.

Row 4: columns 5,6,7 → 3.

Row 5: columns 5,6,7 → 3.

Row 6: columns 5,6,7 → 3.

Now sum these: 5+3+3+3+3+3 = 5 + 15 = 20. Wait, but let's check again. Wait, maybe the number of rows for the vertical part is 5? Row 2 to row 6 is 5 rows (2,3,4,5,6: 5 rows). And 3 columns (5,6,7: 3 columns). So 3*5 = 15. Plus the top row (5) gives 20.

Alternatively, we can use the formula for the area of a composite figure. The figure can be seen as a rectangle of length 5 and height 1 (area 5*1 = 5) plus a rectangle of length 3 and height 5 (area 3*5 = 15). Then total area is 5 + 15 = 20.

Step2: Verify

Let's count the squares again. Let's mark each square:

Top row (row 1): 5 squares (correct, columns 3 - 7).

Row 2: columns 5 - 7 → 3 (correct).

Row 3: columns 5 - 7 → 3 (correct).

Row 4: columns 5 - 7 → 3 (correct).

Row 5: columns 5 - 7 → 3 (correct).

Row 6: columns 5 - 7 → 3 (correct).

Sum: 5+3+3+3+3+3 = 20. So the area is 20 square units.

Answer:

20