Question

find the area of the polygon. a 33 square units b 45 square units

Explanation:

Step1: Count squares in left part

The left rectangular part: width 3, height 5. Area = \(3\times5 = 15\)

Step2: Count squares in middle part

Middle rectangular part: width 4, height 3. Area = \(4\times3 = 12\)

Step3: Count squares in right part

Right rectangular part: width 3, height 2. Area = \(3\times2 = 6\) Wait, no, re - evaluate the figure. Let's count each square:

Alternative approach: Count the number of unit squares.

First block (top left): 3 columns and 5 rows? Wait, no, looking at the grid, let's count row by row.

Row 1 (top of the yellow figure): 3 squares.

Row 2: 3 squares.

Row 3: 7 squares (3 + 4).

Row 4: 7 squares.

Row 5: 7 squares? No, wait, let's do it properly.

Wait, the figure can be divided into three parts:

1. Top - left rectangle: 3 columns (x - direction) and 5 rows (y - direction)? No, actually, let's count the number of unit squares:

Looking at the grid, each small square is 1 unit².

First, the left - most vertical block: from x = 2 to x = 4 (3 units) and y = 1 to y = 5 (5 units), so \(3\times5=15\)

Then, the middle block: from x = 4 to x = 8 (4 units) and y = 3 to y = 5 (3 units), so \(4\times3 = 12\)

Then, the bottom - right block: from x = 5 to x = 7 (3 units) and y = 6 to y = 8 (3 units)? Wait, no, maybe a better way is to count all the yellow squares:

Let's list the number of squares in each row (from top to bottom of the yellow figure):

Row 1 (highest row of yellow): 3 squares.

Row 2: 3 squares.

Row 3: 7 squares (3 + 4, since the middle part starts here).

Row 4: 7 squares.

Row 5: 7 squares? No, that's not right. Wait, maybe the correct way is:

The first rectangle (left) has dimensions 3 (width) and 5 (height): \(3\times5 = 15\)

The second rectangle (middle) has dimensions 4 (width) and 3 (height): \(4\times3=12\)

The third rectangle (right - bottom) has dimensions 3 (width) and 2 (height)? No, wait, let's count the total number of squares:

Wait, 3 (first column of left) * 5 (rows) = 15

Then, the middle part: from column 4 to column 7 (4 columns) and rows 3 to 5 (3 rows): 4*3 = 12

Then, the bottom - right part: column 5 to column 7 (3 columns) and rows 6 to 7 (2 rows)? No, maybe I made a mistake. Let's count the squares one by one:

Looking at the figure, the total number of yellow squares:

First, the left vertical strip: 3 columns (x = 2,3,4) and 5 rows (y = 1,2,3,4,5) → 3*5 = 15

Then, the middle horizontal strip: from x = 4 to x = 7 (4 columns) and y = 3 to y = 5 (3 rows) → 4*3 = 12

Then, the bottom - right strip: from x = 5 to x = 7 (3 columns) and y = 6 to y = 7 (2 rows)? No, wait, when we add 15+12 = 27, then the bottom - right part: 3*3 = 9? Wait, 15+12 + 9=36? No, the options are 33 and 45.

Wait, maybe a better approach: Let's count the number of squares in each row of the yellow polygon:

Row 1 (top row of yellow): 3 squares.

Row 2: 3 squares.

Row 3: 7 squares (3 + 4).

Row 4: 7 squares.

Row 5: 7 squares? No, that's 3+3 + 7+7+7=27, which is not matching. Wait, maybe the figure is:

Wait, the left part: 3 columns and 5 rows (3*5 = 15)

The middle part: 4 columns and 3 rows (4*3 = 12)

The right - bottom part: 3 columns and 2 rows? No, 15+12+6 = 33. Ah, that's option A.

Wait, let's check again. Let's count the number of unit squares:

• The top - left rectangle: 3 (width) × 5 (height) = 15.

• The middle rectangle: 4 (width) × 3 (height) = 12.

• The bottom - right rectangle: 3 (width) × 2 (height) = 6.

Total area: 15 + 12+6 = 33.

Answer:

A. 33 square units