Question

what is the area of this figure?
8 m
3 m
4 m
9 m
6 m
5 m
4 m
8 m
8 m
3 m
square meters
submit

Explanation:

Step1: Divide the figure into three rectangles

We can split the composite figure into three rectangles: the top - left large rectangle, the top - right rectangle, and the bottom rectangle.

Step2: Calculate the area of the top - left rectangle

The length of the top - left rectangle: Let's find the length. The total horizontal length from the left - most to the point before the top - right rectangle: we know that the bottom part has a width of 3m, and the left part (before the bottom rectangle) has a length of 5m and the right part (before the bottom rectangle) has a length of 4m. Wait, actually, for the top - left rectangle, the height is 9m, and the width: let's see, the top - left rectangle's width can be calculated as follows. The top side of the top - left rectangle is 8m, and the vertical side: the height of the top - left rectangle is 9m. Wait, maybe a better way:

First rectangle (top - left):
Height \( h_1=9m \)
Width \( w_1 \): Let's find the width. The bottom rectangle has a width of 3m. The left part (horizontal) of the top - left rectangle: from the left, we have 5m, and the right part (horizontal) of the top - left rectangle: the top - right rectangle has a width of 4m, but the top - left rectangle's width can be found by considering the horizontal dimensions. Wait, actually, the top - left rectangle: the height is 9m, and the width is \( 5 + 3=8m \)? Wait, no. Wait, the figure:

Wait, let's re - divide:

1. Top - left rectangle: height = 9m, width = 8m (since the top side is 8m and the left side is 9m)
2. Top - right rectangle: height = 6m, width = 4m
3. Bottom rectangle: height = 8m, width = 3m

Wait, no, maybe my initial division is wrong. Let's do it properly.

Alternative division:

First rectangle: the large rectangle on the left - top with height 9m and width \( 5 + 3=8m \) (because the bottom rectangle has width 3m, and the left part of the top has 5m, so total width for the left - top rectangle is 5 + 3 = 8m? Wait, no, the top - left rectangle's top side is 8m, so width is 8m, height is 9m.

Second rectangle: the right - top rectangle with height 6m and width 4m.

Third rectangle: the bottom rectangle with height 8m and width 3m.

Wait, let's check the vertical dimensions. The top - left rectangle has height 9m, the top - right rectangle has height 6m, and the bottom rectangle has height 8m.

Now, calculate the area of each rectangle:

Area of first rectangle (top - left): \( A_1=8\times9 = 72m^2 \)

Area of second rectangle (top - right): \( A_2 = 4\times6=24m^2 \)

Area of third rectangle (bottom): \( A_3=3\times8 = 24m^2 \)

Wait, but wait, is there an overlap? No, because we are dividing the figure into non - overlapping rectangles.

Wait, let's verify the horizontal and vertical dimensions.

For the top - left rectangle: width 8m, height 9m.

Top - right rectangle: width 4m, height 6m. The vertical position: the top - right rectangle's height is 6m, and the top - left rectangle's height is 9m, so the vertical difference is \( 9 - 6=3m \), which matches the 3m shown on the figure.

Bottom rectangle: width 3m, height 8m. The horizontal position: it is centered? Wait, the bottom rectangle's width is 3m, and the horizontal length of the bottom part: the left part (horizontal) is 5m, the right part (horizontal) is 4m, and 5+3 + 4=12m, and the top - left rectangle's width is 8m, top - right rectangle's width is 4m, 8 + 4=12m, which matches. The vertical length of the bottom rectangle: 8m, and the vertical length from the bottom of the top - left and top - right rectangles to the bottom of the bottom rectangle is 8m, which matches.

So now, calculate each area:

Area of first rectangle (top - left): \( A_1=8\times9 = 72m^2 \)

Area of second rectangle (top - right): \( A_2=4\times6 = 24m^2 \)

Area of third rectangle (bottom): \( A_3=3\times8 = 24m^2 \)

Wait, but that can't be right. Wait, maybe the first rectangle is height 9m and width \( 5 + 3=8m \) (since the bottom rectangle has width 3m, and the left part of the top has 5m). The second rectangle: height 6m and width 4m. The third rectangle: height 8m and width 3m.

Now, sum the areas:

\( A = A_1+A_2 + A_3=8\times9+4\times6 + 3\times8 \)

Step3: Calculate each term

\( 8\times9 = 72 \)

\( 4\times6=24 \)

\( 3\times8 = 24 \)

Step4: Sum the areas

\( A=72 + 24+24=120 \)

Wait, but let's check again. Maybe my division is wrong. Let's try another division.

Alternative division:

1. Rectangle 1: height = 9m, width = 8m (area \( 8\times9 = 72 \))
2. Rectangle 2: height = 6m, width = 4m (area \( 4\times6 = 24 \))
3. Rectangle 3: height = 8m, width = 3m (area \( 3\times8 = 24 \))

Total area: \( 72+24 + 24=120 \) square meters.

Answer:

120