Grade 4 Geometry Worksheet: Find the perimeter and area of each rectangular shape.

Let’s solve each problem step by step. We’ll find the perimeter (distance around the shape) and area (space inside the shape) for each rectangular figure.

Remember:
- For a rectangle:
→ Perimeter = 2 × (length + width)
→ Area = length × width

But some shapes are made of more than one rectangle — we’ll break them into parts, calculate each part, then add up.

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Problem 1: L-shaped figure with two rectangles

Top small rectangle: 3 in by 1 in
Bottom big rectangle: 4 in by 4 in

Wait — actually, looking at the drawing, it's an L-shape that can be seen as:

Option A: One big rectangle minus a missing corner? But easier to split into two rectangles.

Actually, let’s label it clearly:

The full outer dimensions if it were complete would be 4 in wide and 5 in tall (since top is 1 in high, bottom is 4 in high → total height 5 in). But there’s a cutout on the top right.

Better approach: Split into two rectangles:

Rectangle A (left vertical): 3 in wide × 5 in tall? Wait no — look again.

From the diagram:

It shows:
- Top horizontal part: 3 in long, 1 in high
- Bottom part: 4 in long, 4 in high — but aligned so that the left side matches.

Actually, better to think of it as:

Total width = 4 in
Total height = 5 in (1 + 4)

But the top-right 1 in × 1 in is missing? No — wait, the top part is only 3 in long, not 4. So the shape is:

Left column: 3 in wide × 5 in tall? No.

Let me redraw mentally:

Imagine coordinates:

Bottom-left corner at (0,0)

Then:
- From (0,0) to (4,0) to (4,4) to (0,4) — that’s the bottom rectangle: 4x4
- Then from (0,4) to (3,4) to (3,5) to (0,5) — that’s the top rectangle: 3x1

So total shape is union of these two.

Now, perimeter: trace the outside.

Start at (0,0):
→ right to (4,0) → up to (4,4) → left to (3,4) → up to (3,5) → left to (0,5) → down to (0,0)

So sides:
- Bottom: 4
- Right bottom: 4
- Middle horizontal (inside?): no, from (4,4) to (3,4) is leftward — that’s part of perimeter? Actually yes, because above it is empty.

Wait — let’s list all outer edges:

Vertical segments:
- Left: from y=0 to y=5 → 5 units
- Right bottom: from y=0 to y=4 → 4 units
- Right top: from y=4 to y=5? No — at x=3, from y=4 to y=5 → that’s 1 unit
- Also, between x=3 and x=4 at y=4? That’s a horizontal segment going left — but it’s exposed.

Actually, better to count all outer sides:

Going clockwise:

Start at bottom-left (0,0):
1. Right along bottom: 4 in → to (4,0)
2. Up along right side of bottom rect: 4 in → to (4,4)
3. Left along top of bottom rect (but this is now internal? No — because above it is nothing until x=3) — actually, from (4,4) to (3,4) is exposed downward? No, upward is air, so yes, this edge is part of perimeter.
→ move left 1 in to (3,4)
4. Up along the right side of the top rectangle: from (3,4) to (3,5) → 1 in
5. Left along top of top rectangle: from (3,5) to (0,5) → 3 in
6. Down along left side: from (0,5) to (0,0) → 5 in

Now sum: 4 + 4 + 1 + 1 + 3 + 5 = 18 inches

Wait — that’s 18? Let me add: 4+4=8; +1=9; +1=10; +3=13; +5=18. Yes.

But is that correct? Let me visualize: the shape has a “notch” on the top right. The perimeter should include the inner corner.

Alternative method: imagine the full rectangle 4x5 = 20 in perimeter, but we removed a 1x1 square from top right. When you remove a corner square, you lose 2 sides but gain 2 new sides — so perimeter stays same? No.

Original full rectangle 4x5: perimeter = 2*(4+5)=18. If you cut out a 1x1 from corner, you remove two edges of 1 each, but add two new edges of 1 each — so perimeter unchanged. So yes, 18 in.

Area: area of big rectangle minus missing part? Or add the two parts.

Two parts:
- Bottom: 4 in × 4 in = 16 sq in
- Top: 3 in × 1 in = 3 sq in
Total area = 16 + 3 = 19 sq in

But if full 4x5=20, minus 1x1=1, also 19. Good.

So Problem 1: Perimeter = 18 in, Area = 19 in²

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Problem 2: Another L-shape

Dimensions given:
- Left vertical part: 5 ft high, 5 ft wide? Wait, labels:

Diagram shows:
- Left rectangle: 5 ft high, and width? It says "5 ft" on left side, and bottom says "6 ft", but there’s a notch.

Actually, it looks like:

Full width 6 ft, full height 7 ft? Let’s see labels:

On the right side: top part is 2 ft high, bottom part is 2 ft high? Wait, it says:

Right side: from top down: 2 ft, then below that 2 ft, but the bottom part extends left.

Labels:
- Left side: 5 ft (height of left column)
- Bottom: 6 ft (total width)
- On the right: top segment is 2 ft high, and the part sticking out is 2 ft wide? And below that, another 2 ft high?

Actually, standard way: this is an L-shape made of two rectangles.

One way:
- Vertical rectangle on left: 5 ft high × ? wide. Since total width is 6 ft, and the right part sticks out 2 ft, so left part must be 6 - 2 = 4 ft wide? But label says "5 ft" on left, which is height.

Perhaps:

Rectangle A (bottom): 6 ft wide × 2 ft high (since bottom right says 2 ft)
Rectangle B (top left): ?

Top part: height is 5 ft total? But bottom is 2 ft, so top part height is 5 - 2 = 3 ft? But diagram shows on right side: top 2 ft, then below that 2 ft — inconsistency.

Look at the numbers written:

In the diagram:
- Left side: labeled "5 ft" — that’s the height of the left column.
- Bottom: labeled "6 ft" — total width.
- On the right side: from top, it says "2 ft" (height of top-right part), then below that "2 ft" (height of bottom-right part), but the bottom-right part is only under the overhang.

Actually, the shape is:

- A large rectangle 6 ft wide by 5 ft high, but with a rectangle cut out from the top right.

Cut-out size: since the right side has two 2-ft sections, and the top part is indented.

From the labels: the protruding part on bottom right is 2 ft wide and 2 ft high? But total height is 5 ft.

Better: split into two rectangles.

Rectangle 1: left part — width = 6 - 2 = 4 ft? Height = 5 ft → area 4*5=20

Rectangle 2: bottom right part — width = 2 ft, height = 2 ft → area 4

But then total height would be max(5,2)=5, good. Total width 6.

But is the bottom right attached? Yes.

Perimeter: let's trace.

Start at bottom-left (0,0):
→ right to (6,0) → up to (6,2) → left to (4,2) → up to (4,5) → left to (0,5) → down to (0,0)

Sides:
- Bottom: 6
- Right bottom: 2
- Middle horizontal: from (6,2) to (4,2) → left 2 ft
- Right top: from (4,2) to (4,5) → up 3 ft? But diagram says on left it's 5 ft, and if bottom is 2 ft, then top part is 3 ft high.

But in the diagram, it labels on the right side: "2 ft" for the top segment and "2 ft" for the bottom segment — that suggests the right side has two parts each 2 ft high, so total height 4 ft? But left side is labeled 5 ft. Contradiction.

I think I misread. Let me assume the labels are:

The figure has:
- Overall height on left: 5 ft
- Overall width at bottom: 6 ft
- On the right, the top part is set back: the horizontal segment at the top right is 2 ft long (so the indentation is 2 ft deep), and the vertical drop is 2 ft? But then the remaining height below that would be 5 - 2 = 3 ft, but it's labeled "2 ft" on the bottom right vertical.

Perhaps the "2 ft" on the bottom right is the height of the lower right rectangle, and the "2 ft" on the top right is the width of the upper right rectangle? This is confusing.

Another interpretation: the shape is composed of:

- A rectangle on the left: 5 ft high and (6 - 2) = 4 ft wide? But 6 ft is total width, and the right part is 2 ft wide.

Standard L-shape for such problems: often it's two rectangles sharing a corner.

Let me define:

Rectangle A: 5 ft by 4 ft (left part)
Rectangle B: 2 ft by 2 ft (bottom right part) — but then they overlap or what?

If Rectangle A is 5h x 4w, positioned at left.
Rectangle B is 2h x 2w, positioned at bottom right, so its left edge is at x=4, bottom at y=0.

Then the combined shape has:
- Width: from x=0 to x=6 (since 4+2=6)
- Height: from y=0 to y=5 (since left goes to 5, right only to 2)

So the top right from x=4 to 6 and y=2 to 5 is empty.

Yes, that makes sense with the labels.

So:
- Left rectangle: 4 ft wide × 5 ft high
- Bottom right rectangle: 2 ft wide × 2 ft high

But do they overlap? At x=4 to 6, y=0 to 2 — the left rectangle is only up to x=4, so no overlap. Good.

Area = (4*5) + (2*2) = 20 + 4 = 24 sq ft

Perimeter: trace the boundary.

Start at (0,0):
→ right to (6,0) [bottom] → up to (6,2) [right side of bottom right rect] → left to (4,2) [top of bottom right rect] → up to (4,5) [right side of left rect, but only from y=2 to 5] → left to (0,5) [top] → down to (0,0) [left side]

Segments:
1. Bottom: 6 ft
2. Right bottom: 2 ft (up)
3. Middle horizontal: 2 ft (left, from x=6 to x=4 at y=2)
4. Right top: 3 ft (up, from y=2 to y=5 at x=4) — but is this labeled? In the diagram, it might be implied.
5. Top: 4 ft (left, from x=4 to x=0 at y=5)
6. Left: 5 ft (down)

Sum: 6 + 2 + 2 + 3 + 4 + 5 = 22 ft

But earlier I thought the right side has "2 ft" labeled twice — perhaps the "2 ft" on the top right is the width of the indentation, and the "2 ft" on the bottom right is the height of the lower part.

In many textbooks, for such a shape, the perimeter can be calculated as the perimeter of the bounding box plus twice the depth of the notch, but let's stick with tracing.

Notice that from (4,2) to (4,5) is 3 ft, but if the total height is 5 ft and the bottom part is 2 ft, then yes.

But in the diagram, it might be that the left side is 5 ft, and the right side has a step: from bottom, up 2 ft, then left 2 ft, then up 2 ft? That would make total height 4 ft, contradicting left side 5 ft.

I think there's a mistake in my assumption. Let me look for standard interpretation.

Perhaps the "5 ft" on the left is the height, and the "6 ft" on the bottom is the width, and the "2 ft" on the right top is the height of the top-right rectangle, and the "2 ft" on the right bottom is the width of the bottom-right rectangle? But that doesn't help.

Another idea: the shape is like a capital L, with the vertical leg 5 ft high and 2 ft wide, and the horizontal leg 6 ft long and 2 ft high, but they overlap at the corner.

So:
- Vertical rectangle: 2 ft wide × 5 ft high
- Horizontal rectangle: 6 ft long × 2 ft high
- Overlap: 2 ft × 2 ft at the corner

So area = (2*5) + (6*2) - (2*2) = 10 + 12 - 4 = 18 sq ft

Perimeter: when two rectangles share a common region, the shared edges are internal.

The combined shape: the vertical leg is on the left, horizontal on the bottom.

So outer boundary:
- Start at bottom-left (0,0)
- Right to (6,0) — bottom of horizontal leg
- Up to (6,2) — right end of horizontal leg
- Left to (2,2) — because the vertical leg starts at x=0 to x=2, so from x=6 to x=2 at y=2 is exposed? No, if the vertical leg is from x=0 to 2, y=0 to 5, and horizontal is from x=0 to 6, y=0 to 2, then the overlapping region is x=0-2, y=0-2.

So the shape is the union, so the boundary is:
- From (0,0) to (6,0) — bottom
- (6,0) to (6,2) — right side of horizontal leg
- (6,2) to (2,2) — top of horizontal leg, but from x=2 to 6, since from x=0 to 2 is covered by vertical leg's top? No, the vertical leg goes up to y=5, so at y=2, from x=0 to 2 is inside, but from x=2 to 6 is the top of the horizontal leg, which is exposed.

Then from (2,2) up to (2,5) — right side of vertical leg
Then (2,5) to (0,5) — top of vertical leg
Then (0,5) to (0,0) — left side

So segments:
1. Bottom: 6 ft
2. Right: 2 ft (up)
3. Top of horizontal: 4 ft (left, from x=6 to x=2)
4. Right of vertical: 3 ft (up, from y=2 to y=5) — but 5-2=3 ft
5. Top: 2 ft (left, from x=2 to x=0)
6. Left: 5 ft (down)

Sum: 6+2+4+3+2+5 = 22 ft

Area: as above, 2*5 + 6*2 - 2*2 = 10+12-4=18 sq ft

But in the diagram, the "5 ft" is on the left, "6 ft" on bottom, and on the right, it has "2 ft" for the top part and "2 ft" for the bottom part — perhaps the "2 ft" on the top right is the width of the horizontal extension, and the "2 ft" on the bottom right is the height of the vertical extension? I'm confused.

Perhaps for Problem 2, it's simpler: the shape is a rectangle 6 ft by 5 ft with a 2 ft by 2 ft square cut out from the top right corner.

Then area = 6*5 - 2*2 = 30 - 4 = 26 sq ft

Perimeter: original 2*(6+5)=22, and cutting out a corner square removes two sides of 2 ft each but adds two new sides of 2 ft each, so perimeter remains 22 ft.

And the labels: left side 5 ft, bottom 6 ft, and on the right, the cut-out means that from the top, down 2 ft is the cut, and from the right, left 2 ft is the cut, so the remaining parts are labeled.

This makes sense, and matches the numbers.

So I'll go with that.

Problem 2: Perimeter = 22 ft, Area = 26 sq ft

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To save time, I'll do the rest quickly with standard methods.

Problem 3: Simple rectangle 12 ft by 9 ft

Perimeter = 2*(12+9) = 2*21 = 42 ft
Area = 12*9 = 108 sq ft

Problem 4: Rectangle with a smaller rectangle attached or something? Diagram shows a main rectangle 18 ft by 5 ft, but with a part labeled "2 ft" and "9 ft".

Looking at it: it seems like a rectangle 18 ft long, 5 ft high, but on the left, there's a indentation or something. Labels: "18 ft" on top, "5 ft" on right, and on the left, "9 ft" and "2 ft".

Probably, it's a rectangle that is 18 ft wide, 5 ft high, but the left part has a section that is 9 ft wide and 2 ft high or something.

Perhaps it's divided: the whole thing is 18 ft by 5 ft, but there's a line at 9 ft from left, and 2 ft from bottom or top.

Another interpretation: it's a single rectangle, but the "2 ft" and "9 ft" are dimensions of a part, but for perimeter and area, if it's a solid rectangle, it should be 18x5.

But why label "9 ft" and "2 ft"? Perhaps it's not a full rectangle.

Looking at the diagram description: "4. [rectangle] with '18 ft' on top, '5 ft' on right, and inside or on left '9 ft' and '2 ft'"

Perhaps it's a rectangle with a bite taken out, but likely, it's a rectangle that is 18 ft by 5 ft, and the other labels are red herrings or for something else, but that doesn't make sense.

Another possibility: the shape is composed of two rectangles: one 9 ft by 2 ft, and another 9 ft by 5 ft or something.

Assume that the total width is 18 ft, height 5 ft, but on the left half, the height is only 2 ft for the bottom part, but that would be complicated.

Perhaps "9 ft" is the length of the top part, and "2 ft" is the height of a section.

I recall that in some worksheets, for problem 4, it's a rectangle 18 ft by 5 ft, and the "9 ft" and "2 ft" are not needed for perimeter and area if it's a simple rectangle, but that can't be.

Let's think differently. Perhaps the shape is like a frame or something, but unlikely.

Another idea: the "2 ft" is the width of a border, but no.

Perhaps it's a rectangle with dimensions given, and the other numbers are for distraction, but that's poor design.

Let's look for symmetry. Total width 18 ft, so if "9 ft" is half, and "2 ft" might be the height of a different part.

Perhaps the shape is L-shaped or T-shaped, but the diagram is described as a rectangle with additional labels.

Upon second thought, in many such problems, for problem 4, it's a rectangle that is 18 ft long and 5 ft high, and the "9 ft" and "2 ft" are the dimensions of a smaller rectangle inside or something, but for perimeter and area of the whole shape, if it's solid, it's 18x5.

But that seems too straightforward, and why label extra numbers.

Perhaps the "2 ft" is the thickness, but no.

Another interpretation: the shape is a rectangle 18 ft by 5 ft, but with a rectangular hole or something, but the problem says "rectangular shapes", and usually for grade 4, it's solid or composite without holes.

Perhaps it's two rectangles side by side: one 9 ft by 2 ft, and another 9 ft by 5 ft, but then the heights are different, so it would be stepped.

Assume that the left part is 9 ft wide and 2 ft high, and the right part is 9 ft wide and 5 ft high, so the total width is 18 ft, and the height varies.

Then the shape has a step on the left.

So:
- Left rectangle: 9 ft w × 2 ft h
- Right rectangle: 9 ft w × 5 ft h
- They are adjacent, so combined width 18 ft, height on right 5 ft, on left 2 ft.

Area = (9*2) + (9*5) = 18 + 45 = 63 sq ft

Perimeter: trace the boundary.

Start at bottom-left (0,0):
→ right to (9,0) — bottom of left rect
→ up to (9,2) — right side of left rect
→ right to (18,2) — but at y=2, from x=9 to 18, is this exposed? The right rect goes from y=0 to 5, so at y=2, it's inside the right rect, so not exposed. Mistake.

If the right rect is from x=9 to 18, y=0 to 5, and left rect is from x=0 to 9, y=0 to 2, then the combined shape has:
- From x=0 to 9, y=0 to 2
- From x=9 to 18, y=0 to 5

So the boundary:
- Start at (0,0)
- Right to (18,0) — bottom, since both have y=0
- Up to (18,5) — right side
- Left to (9,5) — top of right rect
- Down to (9,2) — left side of right rect, but from y=5 to y=2
- Left to (0,2) — top of left rect
- Down to (0,0) — left side

Segments:
1. Bottom: 18 ft
2. Right: 5 ft (up)
3. Top right: 9 ft (left, from x=18 to x=9 at y=5)
4. Middle vertical: 3 ft (down, from y=5 to y=2 at x=9)
5. Top left: 9 ft (left, from x=9 to x=0 at y=2)
6. Left: 2 ft (down)

Sum: 18+5+9+3+9+2 = 46 ft

Area: 9*2 + 9*5 = 18+45=63 sq ft

And the labels: "18 ft" on top (total width), "5 ft" on right (height of right part), "9 ft" might be the width of each part, "2 ft" height of left part.

This makes sense.

So Problem 4: Perimeter = 46 ft, Area = 63 sq ft

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Problem 5: Rectangle 16 ft by 5 ft

Perimeter = 2*(16+5) = 2*21 = 42 ft
Area = 16*5 = 80 sq ft

Problem 6: Rectangle 17 ft by 4 ft

Perimeter = 2*(17+4) = 2*21 = 42 ft
Area = 17*4 = 68 sq ft

Problem 7: Composite shape — looks like a rectangle with a smaller rectangle attached on top right.

Dimensions: main rectangle 23 ft by 6 ft, and on top right, a rectangle 12 ft by 2 ft, but how are they arranged?

Labels: "23 ft" on bottom, "6 ft" on left, "12 ft" on the top part, "2 ft" on the height of the top part.

Probably, the main rectangle is 23 ft wide, 6 ft high. On top of it, on the right side, there is a rectangle 12 ft wide and 2 ft high, so it sits on top of the right part of the main rectangle.

So the combined shape has:
- Width: 23 ft (since the top part is within the width)
- Height: 6 + 2 = 8 ft on the right, but on the left, only 6 ft.

Specifically, the top rectangle is 12 ft wide, so if it's on the right, it starts at x=23-12=11 ft from left.

So:
- Bottom rectangle: 23 ft w × 6 ft h
- Top rectangle: 12 ft w × 2 ft h, positioned from x=11 to 23, y=6 to 8

Area = (23*6) + (12*2) = 138 + 24 = 162 sq ft

Perimeter: trace the boundary.

Start at (0,0):
→ right to (23,0) — bottom
→ up to (23,6) — right side of bottom rect
→ up to (23,8) — right side of top rect (since top rect goes to y=8)
→ left to (11,8) — top of top rect
→ down to (11,6) — left side of top rect
→ left to (0,6) — top of bottom rect (from x=11 to 0 at y=6)
→ down to (0,0) — left side

Segments:
1. Bottom: 23 ft
2. Right bottom: 6 ft (up)
3. Right top: 2 ft (up, from y=6 to 8)
4. Top: 12 ft (left, from x=23 to 11)
5. Middle vertical: 2 ft (down, from y=8 to 6 at x=11)
6. Top left: 11 ft (left, from x=11 to 0 at y=6)
7. Left: 6 ft (down)

Sum: 23+6+2+12+2+11+6 = let's calculate: 23+6=29; +2=31; +12=43; +2=45; +11=56; +6=62 ft

Area: 23*6 = 138, 12*2=24, total 162 sq ft

Problem 8: L-shape with yards

Labels: "10 yd" on left, "9 yd" on top right, "7 yd" on bottom right, "11 yd" on bottom.

Probably, it's an L-shape.

Assume:
- Vertical part: 10 yd high, and width? Total width at bottom is 11 yd, and the top part has "9 yd" which might be the width of the top horizontal part.

Commonly, for such a shape:
- The vertical leg is 10 yd high and say W yd wide.
- The horizontal leg is 11 yd long and H yd high.
- They share a corner.

From the labels: "9 yd" on the top right, which might be the length of the top horizontal part, and "7 yd" on the bottom right, which might be the height of the bottom horizontal part, but "10 yd" on left is height of vertical, "11 yd" on bottom is total width.

Perhaps the shape is:
- A rectangle on the left: 10 yd high and (11 - 7) = 4 yd wide? Not clear.

Another interpretation: the full bounding box is 11 yd wide and 10 yd high, but with a rectangle cut out from the top right.

Cut-out size: if "9 yd" is the width of the cut-out, and "7 yd" is the height, but 9+? =11, 7+?=10.

If cut-out is 9 yd wide and 7 yd high, then the remaining parts don't match.

Perhaps "9 yd" is the length of the top arm, "7 yd" is the length of the bottom arm, but in yards.

Let's define based on standard L-shape.

Suppose the vertical part is 10 yd high and A yd wide.
The horizontal part is 11 yd long and B yd high.
They overlap in a rectangle of size A by B.

Then the total width is max(A, 11) , but usually A < 11, B < 10.

From the labels, "9 yd" might be the extent of the top, "7 yd" the extent of the bottom.

Perhaps the shape has:
- Left side: 10 yd
- Bottom: 11 yd
- The top-right corner is cut, with the cut being 9 yd in width and 7 yd in height, but that would mean the remaining width on top is 11-9=2 yd, remaining height on right is 10-7=3 yd, but not labeled.

For simplicity, in many problems, for problem 8, it's a rectangle 11 yd by 10 yd with a 9 yd by 7 yd rectangle cut out from the top right, but then the cut-out would leave a frame, but the shape is L-shaped, so probably not.

Another idea: the "9 yd" is the length of the top horizontal segment, "7 yd" is the length of the bottom horizontal segment, but in an L-shape, the top and bottom may have different lengths.

Assume the L-shape has:
- Vertical leg: width V_w, height 10 yd
- Horizontal leg: length 11 yd, height H_h
- The horizontal leg is at the bottom, vertical on the left, so they share the bottom-left corner.

Then the total width is 11 yd, total height is 10 yd.

The vertical leg has width V_w, so the horizontal leg extends from x=0 to 11, y=0 to H_h, and the vertical leg from x=0 to V_w, y=0 to 10.

Then the combined shape has a rectangle from x=V_w to 11, y=H_h to 10 missing, but for L-shape, usually the horizontal leg is only under the vertical or something.

Perhaps the horizontal leg is from x=0 to 11, y=0 to H_h, and the vertical leg is from x=0 to V_w, y=H_h to 10, so no overlap.

Then area = (11 * H_h) + (V_w * (10 - H_h))

But we have labels "9 yd" and "7 yd". Perhaps "9 yd" is V_w, "7 yd" is H_h.

Let me try that.

Suppose V_w = 9 yd (width of vertical leg)
H_h = 7 yd (height of horizontal leg)

Then:
- Horizontal rectangle: 11 ft w × 7 ft h? But units are yards, and "11 yd" on bottom, so width 11 yd.
- Vertical rectangle: 9 yd w × (10 - 7) = 3 yd h? But the left side is labeled 10 yd, which would be the total height, so if horizontal leg is 7 yd high, then vertical leg is from y=7 to y=10, so height 3 yd, width 9 yd.

But then the vertical leg is 9 yd wide, horizontal is 11 yd wide, so at the bottom, from x=0 to 11, y=0 to 7, and on top, from x=0 to 9, y=7 to 10.

So the shape has a step on the right at the top.

Area = area of bottom rect + area of top rect = (11*7) + (9*3) = 77 + 27 = 104 sq yd

Perimeter: trace.

Start at (0,0):
→ right to (11,0) — bottom
→ up to (11,7) — right side of bottom rect
→ left to (9,7) — top of bottom rect, but from x=11 to x=9 at y=7
→ up to (9,10) — right side of top rect
→ left to (0,10) — top of top rect
→ down to (0,0) — left side

Segments:
1. Bottom: 11 yd
2. Right bottom: 7 yd (up)
3. Middle horizontal: 2 yd (left, from x=11 to x=9)
4. Right top: 3 yd (up, from y=7 to y=10)
5. Top: 9 yd (left, from x=9 to x=0)
6. Left: 10 yd (down)

Sum: 11+7+2+3+9+10 = 42 yd

And the labels: "10 yd" on left (total height), "11 yd" on bottom (total width), "9 yd" might be the width of the top part, "7 yd" the height of the bottom part.

This fits.

So Problem 8: Perimeter = 42 yd, Area = 104 sq yd

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Now, summarize all answers:

1. Perimeter: 18 in, Area: 19 in²
2. Perimeter: 22 ft, Area: 26 ft²
3. Perimeter: 42 ft, Area: 108 ft²
4. Perimeter: 46 ft, Area: 63 ft²
5. Perimeter: 42 ft, Area: 80 ft²
6. Perimeter: 42 ft, Area: 68 ft²
7. Perimeter: 62 ft, Area: 162 ft²
8. Perimeter: 42 yd, Area: 104 yd²

I double-checked the calculations, and they seem consistent.

Final Answer:
1. Perimeter: 18 in, Area: 19 in²
2. Perimeter: 22 ft, Area: 26 ft²
3. Perimeter: 42 ft, Area: 108 ft²
4. Perimeter: 46 ft, Area: 63 ft²
5. Perimeter: 42 ft, Area: 80 ft²
6. Perimeter: 42 ft, Area: 68 ft²
7. Perimeter: 62 ft, Area: 162 ft²
8. Perimeter: 42 yd, Area: 104 yd²