Question

what is the area of this figure? 3 yd 3 yd 5 yd 2 yd 5 yd 2 yd 4 yd 15 yd 8 yd 7 yd square yards

Explanation:

Step1: Analyze the figure's components

The figure can be considered as a large rectangle with some smaller rectangles added or subtracted? Wait, actually, let's break it into parts. Wait, maybe a better approach: the main vertical rectangle, and the two horizontal rectangles on top, and subtract the white rectangle? Wait, no, looking at the dimensions:

Wait, the large vertical rectangle: height 15 yd, width 7 yd? Wait, no, the bottom part is 8 yd height, 7 yd width? Wait, maybe I misread. Wait, the figure has a bottom rectangle (8 yd height, 7 yd width), a middle part, and a top part. Wait, alternatively, let's use the "add the areas of the green parts and subtract the white part".

Wait, the white rectangle has dimensions 5 yd (length) and 2 yd (width)? Wait, no, the white rectangle is 4 yd and 2 yd? Wait, the white rectangle is labeled 5 yd, 4 yd, 2 yd. Wait, maybe the figure is composed of:

1. A large rectangle with height 15 yd and width 7 yd? Wait, no, the bottom rectangle is 8 yd high, 7 yd wide. Then above it, there's a section, and then a top rectangle. Wait, maybe better to calculate the area of the green regions by adding the areas of the three green rectangles and subtracting the white rectangle? Wait, no, the white rectangle is a cut-out? Wait, no, the green figure: let's see the dimensions.

Wait, the rightmost vertical side is 15 yd. The bottom green rectangle: height 8 yd, width 7 yd. Then above it, there's a green rectangle? Wait, no, the middle part: the white rectangle is 4 yd (length) and 2 yd (width), and above that, a green rectangle with height 2 yd and length 5 yd? Wait, maybe I should use the method of "total area of the outer rectangle minus the area of the white rectangle".

Wait, let's find the outer dimensions. The total height is 15 yd, total width: let's see, the bottom width is 7 yd, the top width is 3 yd? No, that doesn't make sense. Wait, maybe the figure is made by:

- A large rectangle with height 15 yd and width 7 yd: area = 15 * 7 = 105 sq yd.

- Then, add the area of the top green rectangle (3 yd x 3 yd? Wait, no, the top green rectangle is 3 yd (width) and (15 - 8 - 2 - 3)? No, this is getting confusing. Wait, maybe another approach:

Looking at the green parts:

1. Bottom green rectangle: height 8 yd, width 7 yd. Area = 8 * 7 = 56 sq yd.

2. Middle green rectangle: height 2 yd, width 5 yd (since it's above the bottom rectangle, and the white rectangle is in between). Wait, no, the middle green rectangle: the white rectangle is 4 yd x 2 yd, so the middle green rectangle (between bottom and top) has length 5 yd, height 2 yd? Wait, maybe:

Wait, the top green rectangle: 3 yd (width) and (15 - 8 - 2) = 5 yd? No, 15 - 8 = 7, 7 - 2 = 5? Wait, 3 yd width, height 3 yd? Wait, the top green rectangle is 3 yd x 3 yd? No, the top green rectangle is 3 yd (width) and (15 - 8 - 2 - 3)? No, I think I'm overcomplicating.

Wait, let's use the formula for the area of a composite figure: add the areas of all green rectangles and subtract the white rectangle.

Green rectangles:

1. Bottom: 8 yd (height) * 7 yd (width) = 56

2. Middle: 2 yd (height) * 5 yd (width) = 10

3. Top: 3 yd (height) * 3 yd (width) = 9

Wait, but then there's a white rectangle: 4 yd (length) * 2 yd (width) = 8

Wait, no, maybe the middle green rectangle is 2 yd * 5 yd, but the white rectangle is 4 yd * 2 yd, so the actual middle green area is 5*2 - 4*2? No, that doesn't make sense. Wait, maybe the correct approach is:

Total area of the figure = area of the large rectangle (15 yd height, 7 yd width) + area of the top green rectangle (3 yd x 3 yd) + area of the middle green rectangle (5 yd x 2 yd) - area of the white rectangle (4 yd x 2 yd)

Wait, let's check:

Large rectangle: 15 * 7 = 105

Top green rectangle: 3 * 3 = 9

Middle green rectangle: 5 * 2 = 10

White rectangle: 4 * 2 = 8

Total area = 105 + 9 + 10 - 8 = 116? Wait, no, that doesn't seem right. Wait, maybe the large rectangle is not 15*7. Wait, the bottom rectangle is 8 yd height, 7 yd width: 8*7=56. Then above it, the height from bottom to top is 15 yd, so the remaining height is 15-8=7 yd. In that 7 yd, there's a middle section (2 yd height) and a top section (3 yd height), so 2+3=5, so 7-5=2? No, this is confusing.

Wait, let's look at the dimensions again:

- Bottom green rectangle: height 8 yd, width 7 yd. Area = 8*7 = 56.

- Middle green rectangle: height 2 yd, width 5 yd. Area = 2*5 = 10.

- Top green rectangle: height 3 yd, width 3 yd. Area = 3*3 = 9.

- White rectangle: height 2 yd, width 4 yd. Area = 2*4 = 8.

Wait, but the middle green rectangle and white rectangle: maybe the middle green rectangle is 5 yd width, but the white rectangle is 4 yd width, so the actual middle green area is 5*2 - 4*2 = 2? No, that's not right. Wait, maybe the figure is:

The total height is 15 yd, total width is 7 yd (bottom) + 5 yd? No, that's not. Wait, maybe the correct way is to calculate the area by adding the three green rectangles and subtracting the white one:

Green rectangles:

1. Bottom: 8*7 = 56

2. Middle: 2*5 = 10

3. Top: 3*3 = 9

White rectangle: 2*4 = 8

Total area = 56 + 10 + 9 - 8 = 67? No, that can't be. Wait, maybe I messed up the dimensions.

Wait, another approach: the figure is composed of:

- A vertical rectangle on the right: height 15 yd, width 3 yd. Area = 15*3 = 45.

- A horizontal rectangle on the left (middle): height 2 yd, width 5 yd. Area = 2*5 = 10.

- A horizontal rectangle on the left (bottom): height 8 yd, width 7 yd. Wait, no, 7 yd is the width of the bottom? Wait, the bottom rectangle is 8 yd height, 7 yd width: 8*7=56. But the vertical rectangle on the right is 15 yd height, 3 yd width: 15*3=45. But 56 + 45 would overlap. Wait, no, the vertical rectangle on the right is part of the bottom rectangle? No, the bottom rectangle is 8 yd height, 7 yd width, and the vertical rectangle on the right is 15 yd height, 3 yd width, so the overlapping area is 8 yd height, 3 yd width. So total area would be 8*7 + (15-8)*3 + 2*5 - 2*4.

Let's calculate that:

- Bottom rectangle: 8*7 = 56

- Vertical rectangle above bottom: (15-8)*3 = 7*3 = 21

- Middle horizontal rectangle: 2*5 = 10

- White rectangle: 2*4 = 8

Total area = 56 + 21 + 10 - 8 = 79? No, that still doesn't seem right.

Wait, maybe the correct dimensions are:

The total height is 15 yd, total width is 7 yd. The white rectangle is 5 yd (length) and 2 yd (width), but with a 4 yd length? Wait, I think I need to look at the figure again. The user provided the figure with:

- Bottom green rectangle: 8 yd (height), 7 yd (width)

- Middle green rectangle: 2 yd (height), 5 yd (width)

- Top green rectangle: 3 yd (height), 3 yd (width)

- White rectangle: 4 yd (length), 2 yd (width)

Wait, maybe the correct calculation is:

Area of bottom green: 8*7 = 56

Area of middle green: 2*5 = 10

Area of top green: 3*3 = 9

Area of white rectangle: 4*2 = 8

Total area = 56 + 10 + 9 - 8 = 67? No, that's not matching. Wait, maybe the white rectangle is 5 yd by 2 yd, not 4 yd. Wait, the white rectangle is labeled 5 yd, 4 yd, 2 yd. Maybe the length is 5 yd, width is 2 yd, but with a 4 yd segment? No, this is confusing.

Wait, let's use the formula for the area of a composite figure by adding all the green parts:

1. Bottom green: height 8 yd, width 7 yd. Area = 8 * 7 = 56.

2. Middle green: height 2 yd, width 5 yd. Area = 2 * 5 = 10.

3. Top green: height 3 yd, width 3 yd. Area = 3 * 3 = 9.

Now, the white rectangle is a cut-out? Wait, no, the white rectangle is inside the green figure? Wait, the green figure has a white rectangle, so we need to subtract its area. The white rectangle has length 4 yd and width 2 yd. Area = 4 * 2 = 8.

So total area = 56 + 10 + 9 - 8 = 67? Wait, but let's check with another method.

Alternatively, the total area of the outer rectangle (if we consider the maximum height and width) is 15 yd (height) * 7 yd (width) = 105. Then, subtract the area of the white rectangle (5 yd * 2 yd = 10? No, the white rectangle is 4 yd * 2 yd = 8) and add the area of the top green rectangle (3 yd * 3 yd = 9) and the middle green rectangle (2 yd * 5 yd = 10). Wait, no, 105 - 8 + 9 + 10 = 116. But that seems too big.

Wait, I think I made a mistake in the outer dimensions. Let's look at the bottom green rectangle: height 8 yd, width 7 yd. The vertical rectangle on the right: height 15 yd, width 3 yd. So the bottom green rectangle is 8 yd height, 7 yd width (area 56), and the vertical rectangle on the right is 15 yd height, 3 yd width (area 45). But they overlap in the bottom 8 yd, so the overlapping area is 8*3=24. So total area from these two: 56 + 45 - 24 = 77. Then, add the middle green rectangle (2 yd height, 5 yd width: area 10) and subtract the white rectangle (2 yd height, 4 yd width: area 8). So 77 + 10 - 8 = 79.

But I'm not sure. Wait, maybe the correct answer is 79. Let's check the calculations again:

- Bottom rectangle: 8*7=56

- Vertical rectangle on right: (15-8)*3=21 (since above the bottom rectangle, the height is 15-8=7 yd, but wait, no, the vertical rectangle is 15 yd height, 3 yd width, so area 15*3=45. But the bottom rectangle is 8*7=56, which includes 8*3=24 of the vertical rectangle. So the non-overlapping part of the vertical rectangle is 45-24=21. So total from bottom and vertical: 56 + 21=77.

- Middle green rectangle: 2*5=10 (this is above the bottom rectangle, to the left of the vertical rectangle)

- White rectangle: 2*4=8 (this is a cut-out from the middle green rectangle)

So total area: 77 + 10 - 8=79.

Yes, that makes sense. So:

Step1: Calculate area of bottom green rectangle

Bottom rectangle: height = 8 yd, width = 7 yd
Area = \( 8 \times 7 = 56 \) square yards

Step2: Calculate area of vertical green rectangle above bottom

Vertical rectangle height = \( 15 - 8 = 7 \) yd, width = 3 yd
Area = \( 7 \times 3 = 21 \) square yards

Step3: Calculate area of middle horizontal green rectangle

Middle rectangle: height = 2 yd, width = 5 yd
Area = \( 2 \times 5 = 10 \) square yards

Step4: Calculate area of white rectangle (cut - out)

White rectangle: height = 2 yd, width = 4 yd
Area = \( 2 \times 4 = 8 \) square yards

Step5: Sum the areas and subtract the white rectangle

Total area = \( 56 + 21 + 10 - 8 \)
\( = 77 + 10 - 8 \)
\( = 87 - 8 \)
\( = 79 \) square yards

Answer:

79