Question

what is the area of this figure? square meters

Explanation:

Step1: Calculate area of large rectangle

The large rectangle has length \(12\) m and width \(9 + 5=14\) m? Wait, no, let's re - examine. Wait, actually, we can use the method of subtracting the white areas from the large rectangle. First, find the area of the large rectangle that would enclose the figure. Wait, another way: divide the green figure into parts.

Wait, let's look at the dimensions. The total height is \(12\) m, total width: let's see, the top part is \(9\) m, then there are some indents. Wait, maybe better to calculate the area of the green figure by adding three rectangles?

Wait, first rectangle: top part, length \(9 + 5 = 14\) m? No, wait the top green rectangle: height \(2\) m, width \(9+5 = 14\) m? Wait, no, the top green part: from the diagram, the top horizontal length is \(9\) m, and then there is a \(5\) m at the bottom. Wait, maybe the figure can be considered as a large rectangle with length \(12\) m and width \(9 + 5=14\) m, minus the two white rectangles.

First, area of large rectangle: \(A_{large}=12\times(9 + 5)=12\times14 = 168\) square meters.

Step2: Calculate area of first white rectangle

The first white rectangle (the vertical one) has height \(7\) m and width \(2\) m. So \(A_{white1}=7\times2 = 14\) square meters.

Step3: Calculate area of second white rectangle

The second white rectangle (the bottom one) has height \(3\) m and width \(2\) m. So \(A_{white2}=3\times2=6\) square meters.

Step4: Calculate area of green figure

Subtract the white areas from the large rectangle: \(A = 168-14 - 6=148\)? Wait, that can't be right. Wait, maybe my initial assumption of the large rectangle is wrong.

Wait, let's try another approach. Let's divide the green figure into three rectangles:

1. Top rectangle: height \(2\) m, width \(9 + 5=14\) m? No, wait the top green part: looking at the horizontal length, the top is \(9\) m, and the bottom right is \(5\) m. Wait, maybe the width of the top rectangle is \(9+5 = 14\) m, height \(2\) m: \(A_1=2\times14 = 28\)

2. Middle rectangle: height \(12 - 2-3=7\) m, width \(9\) m? Wait, no. Wait, the middle part: from the top \(2\) m down, then the vertical white rectangle is \(7\) m, then the bottom white is \(3\) m. Wait, maybe the middle green rectangle has height \(7\) m, width \(9\) m: \(A_2 = 7\times9=63\)

3. Bottom rectangle: height \(3\) m, width \(5\) m? No, the bottom green part: width \(5\) m, height \(3\) m? Wait, no, the bottom green rectangle: height \(3\) m, width \(9 + 5=14\) m? No, this is getting confusing.

Wait, let's use the correct method of adding the areas of the green parts. Let's look at the coordinates (imagining the figure):

- Top green rectangle: length \(9 + 5=14\) m, height \(2\) m. Area \(=14\times2 = 28\)

- Middle green rectangle: length \(9\) m, height \(7\) m (since total height is \(12\), minus top \(2\) and bottom \(3\): \(12-2 - 3=7\)). Area \(=9\times7 = 63\)

- Bottom green rectangle: length \(5\) m, height \(3\) m. Area \(=5\times3 = 15\)

Now sum these up: \(28+63 + 15=106\)? Wait, no, that's not right. Wait, maybe the middle rectangle's width is not \(9\). Wait, let's look at the horizontal dimensions. The top green part has a horizontal length of \(9\) m (left to right), and then the bottom right has \(5\) m. The vertical white rectangle is \(2\) m wide (left side), and the bottom white is \(2\) m wide (left side of the bottom).

Wait, another way: The figure can be seen as a rectangle with length \(12\) m and width \(9 + 5=14\) m, minus two white rectangles: one with dimensions \(7\times2\) and one with \(3\times2\).

Wait, let's check the total width: the top horizontal line is \(9\) m, the bottom horizontal line is \(5\) m, and the indented parts are \(2\) m wide. So the total width of the enclosing rectangle is \(9 + 2+5=16\)? No, this is too confusing. Wait, let's look at the given dimensions again:

- The right side height is \(12\) m.

- The bottom right has \(5\) m (horizontal), \(3\) m (vertical).

- The top has \(9\) m (horizontal), \(2\) m (vertical).

- The left has a vertical white rectangle with \(7\) m (vertical), \(2\) m (horizontal), and a bottom white rectangle with \(3\) m (vertical), \(2\) m (horizontal).

Wait, let's calculate the area by adding:

1. Top green rectangle: height \(2\) m, width \(9 + 5=14\) m. Area \(=2\times14 = 28\)

2. Middle green rectangle: height \(7\) m (12 - 2 - 3), width \(9\) m. Area \(=7\times9 = 63\)

3. Bottom green rectangle: height \(3\) m, width \(5\) m. Area \(=3\times5 = 15\)

Wait, but then there is a part between the middle and bottom? No, maybe the middle rectangle's width is \(9 + 2\)? No, I think I made a mistake.

Wait, let's use the method of subtracting the white areas from the large rectangle that would cover the entire figure. The large rectangle would have:

- Height: \(12\) m

- Width: \(9 + 2+5=16\) m? No, the left indents are \(2\) m (vertical white) and \(2\) m (bottom white). Wait, the vertical white rectangle is \(2\) m wide (horizontal) and \(7\) m tall (vertical). The bottom white rectangle is \(2\) m wide (horizontal) and \(3\) m tall (vertical).

The large rectangle that encloses the green figure would have:

- Height: \(12\) m

- Width: \(9 + 5=14\) m? No, the top green is \(9\) m, the bottom green is \(5\) m, and the indents are \(2\) m on the left. So the total width of the enclosing rectangle is \(9+2 + 5=16\) m? No, this is not working.

Wait, let's look at the correct way. Let's calculate the area by adding three rectangles:

1. Top rectangle: height \(2\) m, width \(9 + 5=14\) m. Area \(=2\times14 = 28\)

2. Middle rectangle: height \(7\) m (12 - 2 - 3), width \(9\) m. Area \(=7\times9 = 63\)

3. Bottom rectangle: height \(3\) m, width \(5\) m. Area \(=3\times5 = 15\)

Wait, but \(28+63 + 15=106\). But let's check with another method. Let's calculate the area of the green figure as a large rectangle minus two white rectangles.

Large rectangle: height \(12\) m, width \(9 + 5=14\) m. Area \(=12\times14 = 168\)

White rectangles:

- First white: \(7\times2 = 14\)

- Second white: \(3\times2 = 6\)

Total white area: \(14 + 6=20\)

Green area: \(168-20 = 148\). Wait, now there is a discrepancy. Which is correct?

Wait, maybe the large rectangle's width is \(9 + 2+5=16\) m. Then large rectangle area: \(12\times16 = 192\)

White areas:

- First white: \(7\times2 = 14\)

- Second white: \(3\times2 = 6\)

Green area: \(192-14 - 6=172\). No, this is worse.

Wait, let's look at the diagram again. The figure has:

- Top green part: height \(2\) m, and the horizontal length: from the left, after the \(2\) m indent, the top green extends \(9\) m, and then the bottom right green extends \(5\) m. So the total width of the top green is \(9 + 5=14\) m, height \(2\) m.

- Then, below the top green, there is a vertical green part: height \(7\) m (since \(12-2 - 3=7\)), and width \(9\) m (because the \(2\) m indent is on the left, so the width here is \(9\) m).

- Then, at the bottom, a green part: height \(3\) m, width \(5\) m.

Now, let's calculate each:

Top: \(2\times14 = 28\)

Middle: \(7\times9 = 63\)

Bottom: \(3\times5 = 15\)

Total: \(28+63 + 15=106\). Wait, but maybe the middle width is \(9 + 2=11\)? No, the indent is \(2\) m on the left, so the middle green width should be \(9\) m (the part not indented).

Wait, another approach: Let's use the coordinates. Let's assume the bottom right corner is at \((0,0)\). Then:

- Top green rectangle: from \(y = 10\) to \(y = 12\) (height \(2\)), \(x = 0\) to \(x = 14\) (width \(14\)). Area \(=2\times14 = 28\)

- Middle green rectangle: from \(y = 3\) to \(y = 10\) (height \(7\)), \(x = 2\) to \(x = 11\) (width \(9\)). Area \(=7\times9 = 63\)

- Bottom green rectangle: from \(y = 0\) to \(y = 3\) (height \(3\)), \(x = 9\) to \(x = 14\) (width \(5\)). Area \(=3\times5 = 15\)

Now sum these: \(28+63 + 15=106\). Yes, this makes sense. So the area is \(106\) square meters.

Wait, but let's check again. The middle green rectangle: \(x\) from \(2\) to \(11\) (width \(9\)), \(y\) from \(3\) to \(10\) (height \(7\)). The bottom green: \(x\) from \(9\) to \(14\) (width \(5\)), \(y\) from \(0\) to \(3\) (height \(3\)). The top green: \(x\) from \(0\) to \(14\) (width \(14\)), \(y\) from \(10\) to \(12\) (height \(2\)).

Yes, so adding them up: \(28+63 + 15 = 106\).

Answer:

\(106\)