Question

what is the area of this figure? 3 m 1 m 4 m 5 m 8 m 4 m 2 m 3 m square meters

Explanation:

Step1: Find the total length of the base

The base can be calculated by adding the lengths of the segments. The top has a segment of 4 m and 3 m, so the total length of the base (if we consider the outer rectangle) would be \(4 + 3=7\) m. Wait, alternatively, we can use the method of subtracting the missing parts from the larger rectangle or adding the areas of the parts. Let's use the method of dividing the figure into parts. Let's consider the figure as a combination of a large rectangle and then adjust for the missing or extra parts. Wait, another way: the figure can be divided into three rectangles. Let's see:

First, the left part: height 5 m, width? Wait, maybe better to calculate the area of the large rectangle that would enclose the figure and then subtract the missing areas, or add the areas of the three rectangles. Wait, looking at the figure, there are three rectangles? Wait, no, let's see:

The top right rectangle: width 3 m, height? Wait, the total height on the right is 8 m. The middle part: let's see, the left side has height 5 m, and the bottom missing part is 2 m, top missing part is 1 m. Wait, maybe a better approach:

The figure can be considered as a large rectangle with length \(4 + 3 = 7\) m and height 8 m, then subtract the area of the top missing rectangle (width 4 m, height 1 m) and the bottom missing rectangle (width 4 m, height 2 m).

Step2: Calculate the area of the large enclosing rectangle

Length of large rectangle: \(4 + 3 = 7\) m, height: 8 m. So area is \(7\times8 = 56\) square meters.

Step3: Calculate the area of the top missing rectangle

Width: 4 m, height: 1 m. Area: \(4\times1 = 4\) square meters.

Step4: Calculate the area of the bottom missing rectangle

Width: 4 m, height: 2 m. Area: \(4\times2 = 8\) square meters.

Step5: Subtract the missing areas from the large rectangle

Total area = Area of large rectangle - Area of top missing - Area of bottom missing. So \(56 - 4 - 8 = 44\)? Wait, no, wait, maybe I made a mistake. Wait, alternatively, let's divide the figure into three rectangles:

1. Left rectangle: height 5 m, width \(4 + 3 - 4\)? No, wait, let's look at the horizontal segments. The bottom part: the width of the left rectangle (the part with height 5 m) is \(4 + 3 - 4\)? No, maybe better to look at the vertical and horizontal dimensions.

Wait, another approach: the figure has three parts:

- The left rectangle: height 5 m, width \(4\) m? No, wait, the left side: from the bottom, the height is 5 m, and the width? Wait, maybe the figure is composed of:

Top right rectangle: width 3 m, height \(8 - 5 + 1 = 4\) m? Wait, no, this is getting confusing. Let's use the method of adding the areas of the three rectangles:

1. The left rectangle: height 5 m, width \(4 + 3 - 4\)? No, let's look at the horizontal lengths. The total width of the figure is \(4 + 3 = 7\) m (since the top has 4 m and 3 m, bottom has 4 m and 3 m). The total height is 8 m. But there are two missing rectangles: top (4 m wide, 1 m tall) and bottom (4 m wide, 2 m tall). So the area of the figure is (7*8) - (4*1) - (4*2) = 56 - 4 - 8 = 44? Wait, but let's check by adding the areas of the three rectangles:

- Middle rectangle: height 5 m, width \(7 - 4 = 3\)? No, wait, maybe:

Wait, the left part: a rectangle with height 5 m, width \(4\) m? No, the left side's width: from the left, the first segment is 4 m (bottom missing part's width) and then 3 m? Wait, no, let's look at the coordinates. Let's assume the bottom left corner is (0,0). Then:

- The bottom missing rectangle: from (0,0) to (4, 2), so area 4*2=8.

- The top missing rectangle: from (0, 8 - 1) to (4, 8), so height 1, width 4, area 4*1=4.

- The remaining part: the large rectangle from (0,0) to (7,8) minus the two missing rectangles. So 7*8 - 4 - 8 = 56 - 12 = 44. Wait, but let's check by adding the areas of the three rectangles:

1. The right rectangle: width 3 m, height 8 m. Area: 3*8=24.

2. The middle rectangle: height 5 m, width \(7 - 3 = 4\) m? Wait, 7 - 3 = 4, so 4*5=20.

3. The top rectangle: width 3 m, height 1 m? No, wait, no. Wait, maybe the middle rectangle is 4 m wide (7 - 3) and 5 m tall, area 20. The right rectangle is 3 m wide and 8 m tall, area 24. Then the top small rectangle: width 3 m, height 1 m? No, the top missing part is 4 m wide, 1 m tall. Wait, I think my initial approach is wrong.

Wait, let's draw the figure mentally:

- The bottom has a missing rectangle of 4m (width) x 2m (height) (so a white rectangle at the bottom left, 4m wide, 2m tall).

- The top has a missing rectangle of 4m (width) x 1m (height) (white rectangle at the top left, 4m wide, 1m tall).

- The remaining area is the area of the large rectangle (7m x 8m) minus these two white rectangles.

So 7*8 = 56.

Top white: 4*1=4.

Bottom white: 4*2=8.

56 - 4 - 8 = 44.

Alternatively, let's calculate the area by adding the three green rectangles:

1. The bottom right rectangle: width 3m, height 2m (since the bottom missing is 2m tall, so from y=0 to y=2, x=4 to x=7: 3m wide, 2m tall. Area: 3*2=6.

2. The middle rectangle: width 7m (4+3), height 5m (from y=2 to y=7, since bottom missing is 2m, top missing is 1m, so 8 - 2 - 1 = 5? Wait, 8 - 2 (bottom) - 1 (top) = 5. So middle rectangle: 7m x 5m = 35.

3. The top right rectangle: width 3m, height 1m (from y=7 to y=8, x=4 to x=7: 3m wide, 1m tall. Area: 3*1=3.

Now add these three areas: 6 + 35 + 3 = 44. Yes, that matches. So the area is 44 square meters.

Answer:

44