Area and Perimeter of Polygons Worksheets - Math Monks - Free Printable

Here are the step-by-step solutions for each problem on the worksheet.

Problem 1

Shape: An L-shape made of two rectangles.
Dimensions: Left side 10 cm, Top 18 cm, Right top part 4 cm, Bottom left part 8 cm.

Step 1: Find the Area
Split the shape into two vertical rectangles.
* Left Rectangle: The width is given as 8 cm. The height is the full left side, which is 10 cm.
* Area = $8 \text{ cm} \times 10 \text{ cm} = 80 \text{ cm}^2$
* Right Rectangle: The total top width is 18 cm. Since the left part is 8 cm, the right part is $18 - 8 = 10 \text{ cm}$. The height is given as 4 cm.
* Area = $10 \text{ cm} \times 4 \text{ cm} = 40 \text{ cm}^2$
* Total Area: $80 + 40 = 120 \text{ cm}^2$

Step 2: Find the Perimeter
Add up all the outside edges. We need to find the missing inner vertical and horizontal sides.
* Missing vertical side (inner): Total height (10) - Top right height (4) = 6 cm.
* Missing horizontal side (inner): Total width (18) - Bottom left width (8) = 10 cm.
* Perimeter: $10 + 18 + 4 + 6 + 10 + 8 = 56 \text{ cm}$
*(Tip: For this type of shape, you can also just do $(10 + 18) \times 2 = 56$)*

Problem 2

Shape: A rectangle with a rectangular notch cut out of the top.
Dimensions: Left 8.5 in, Top left 4 in, Notch depth 2.5 in, Notch width 6 in, Top right 4 in.

Step 1: Find the Area
Imagine the full big rectangle first, then subtract the empty notch.
* Full Width: $4 + 6 + 4 = 14 \text{ in}$.
* Full Height: 8.5 in.
* Area of Full Rectangle: $14 \times 8.5 = 119 \text{ in}^2$.
* Area of Notch (empty space): $6 \text{ in} \times 2.5 \text{ in} = 15 \text{ in}^2$.
* Total Area: $119 - 15 = 104 \text{ in}^2$.

Step 2: Find the Perimeter
Add all outer edges.
* Bottom: 14 in (same as total top width).
* Sides: 8.5 in each.
* Top parts: 4 in + 4 in = 8 in.
* Notch sides: There are two vertical sides going down into the notch. Each is 2.5 in.
* Notch bottom: 6 in.
* Perimeter: $14 \text{ (bottom)} + 8.5 \text{ (left)} + 4 \text{ (top)} + 2.5 \text{ (down)} + 6 \text{ (across)} + 2.5 \text{ (up)} + 4 \text{ (top)} + 8.5 \text{ (right)} = 50 \text{ in}$.

Problem 3

Shape: An inverted L-shape.
Dimensions: Top 12 in, Left top 7 in, Inner corner horizontal 6 in, Right side 19 in.

Step 1: Find the Area
Split into two vertical rectangles.
* Left Rectangle: Width is not explicitly given, but we can find it. Total width at top is 12. The "Inner corner horizontal" label of 6 in usually refers to the protruding part or the gap. Looking at the diagram, the bottom-right block sticks out. Let's split it horizontally instead, it's easier.
* Top Rectangle: Width 12 in, Height 7 in. Area = $12 \times 7 = 84 \text{ in}^2$.
* Bottom Rectangle: We need its dimensions. The total height on the right is 19 in. The top part is 7 in, so the bottom part's height is $19 - 7 = 12 \text{ in}$. The width of this bottom sticking-out part is labeled 6 in. Area = $6 \times 12 = 72 \text{ in}^2$.
* Wait, let's look closer. The label "6 in" is on the horizontal segment of the inner corner. This means the width of the right-hand vertical column is 6 in? Or is it the width of the empty space? Usually, in these diagrams, the number next to a line segment is the length of that segment. So the horizontal shelf is 6 in.
* Let's try splitting vertically.
* Left Column: Height is 19? No, the left side only has a 7in segment labeled. The total height is defined by the right side (19 in). So the left column height is 19? No, the shape is an inverted L. The left side goes down 7 inches. Then it goes right. Then it goes down.
* Let's assume the standard interpretation:
* Top horizontal bar: 12 in wide.
* Left vertical drop: 7 in.
* Right vertical total: 19 in.
* Inner horizontal step: 6 in.
* This implies the width of the right vertical leg is 6 in? Or is the remaining width 6 in? If the top is 12 and the inner step is 6, the left part is $12-6=6$? Or is the inner step the width of the right leg? Let's assume the segment labeled "6 in" is the horizontal part connecting the left wall to the right wall.
* So, Left Rectangle Width = $12 - 6 = 6 \text{ in}$. Height = 19 in? No, the left side stops at 7.
* Let's split into:
1. Top Left Rectangle: Width = ? Height = 7.
2. Right Vertical Rectangle: Width = 6? Height = 19.
If the right rectangle is 6 wide, then the top left part is $12 - 6 = 6$ wide.
Area 1 (Right): $6 \times 19 = 114$.
Area 2 (Top Left): $6 \times 7 = 42$.
Total Area = $114 + 42 = 156 \text{ in}^2$.
* Let's check the other interpretation: Maybe the "6 in" is the width of the left part? If left part is 6, right part is $12-6=6$. Same result.
* Let's check if "6 in" is the empty space? Unlikely.
* Let's assume the segment labeled 6 in is the horizontal connector.
* Area = (Left Part $6 \times 7$) + (Right Part $6 \times 19$)? No, that double counts or misses.
* Let's split horizontally:
* Top Bar: $12 \text{ in} \times 7 \text{ in} = 84 \text{ in}^2$.
* Bottom Leg: The total height is 19. The top bar took 7. So the remaining height is $19 - 7 = 12 \text{ in}$. The width of this leg is the remaining width. If the top is 12, and the left part of the top corresponds to the left wall... wait. The diagram shows the left wall is 7 high. Then a step. The step is 6 long. Then the right wall goes down to 19.
* This means the right vertical section has a width of 6 in? No, the 6 in is the horizontal step.
* So, Width of Right Leg = 6 in? If so, Width of Left Leg = $12 - 6 = 6$ in.
* Area = (Top Left $6 \times 7$) + (Right Full Height $6 \times 19$).
* Area = $42 + 114 = 156 \text{ in}^2$.

Step 2: Find the Perimeter
* Top: 12
* Right: 19
* Bottom: Width of right leg (6) + Width of left leg (6) = 12? No, the bottom is just the width of the right leg if it's an inverted L? No, an inverted L has a bottom on the right and a bottom on the left? No, it's one continuous polygon.
* Let's trace the perimeter:
* Top: 12
* Right Side: 19
* Bottom: This is the bottom of the right leg. Width = 6.
* Inner Vertical Up: Height = $19 - 7 = 12$.
* Inner Horizontal Left: 6.
* Left Side: 7.
* Sum: $12 + 19 + 6 + 12 + 6 + 7 = 62 \text{ in}$.

Problem 4

Shape: L-shape.
Dimensions: Top 16.8 ft, Right 13.2 ft, Bottom 12.4 ft, Left bottom 5.1 ft, Left top 8.1 ft. Note: $5.1 + 8.1 = 13.2$. This matches the right side. Good.

Step 1: Find the Area
Split into two vertical rectangles.
* Right Rectangle: Width? Total top is 16.8. Bottom left is 12.4? No, bottom label is 12.4 for the whole bottom? Or just the left part? Usually, the label under a segment applies to that segment. The label "12.4 ft" is under the left-ish part. But looking at the alignment, 12.4 seems to be the width of the wider bottom part. Let's look at the top. Top is 16.8.
* Let's split horizontally.
* Top Rectangle: Height 8.1 ft. Width 16.8 ft. Area = $16.8 \times 8.1 = 136.08 \text{ ft}^2$.
* Bottom Rectangle: Height 5.1 ft. Width? The total width at the top is 16.8. The vertical line drops down from the top right? No, it's an L shape on the bottom left?
* Let's look at the labels again. Left side has two segments: 8.1 and 5.1. Total height = 13.2. This matches the Right side (13.2).
* Top side: 16.8.
* Bottom side: 12.4. This label is under the left portion of the bottom.
* This implies the shape is composed of a tall left part and a short right part? Or a wide top and narrow bottom?
* Visually, it looks like a large rectangle with a chunk missing from the bottom right.
* Let's assume the "12.4 ft" is the width of the bottom-left vertical column.
* So, Left Column: Width 12.4 ft, Height 13.2 ft ($8.1+5.1$). Area = $12.4 \times 13.2 = 163.68 \text{ ft}^2$.
* Right Part: The top extends further. Total top width is 16.8. Left width is 12.4. So the right extension width is $16.8 - 12.4 = 4.4 \text{ ft}$.
* The height of this right extension corresponds to the top segment of the left side? No, the right side is 13.2 total. The "cutout" is at the bottom right.
* Actually, usually these L-shapes are simpler. Let's split it into two rectangles:
1. Left Vertical Rectangle: Width 12.4 ft. Height 13.2 ft? No, the top right sticks out.
2. Let's split vertically at the corner.
* Left Rectangle: Width 12.4 ft. Height = Total Height = 13.2 ft. Area = $12.4 \times 13.2 = 163.68$.
* Right Rectangle: Width = $16.8 - 12.4 = 4.4 \text{ ft}$. Height = Top part only? The right side label is 13.2. This suggests the right edge is fully 13.2 long. But the shape is an L.
* Let's re-read the shape. It looks like a standard L.
* Left Wall: 8.1 + 5.1 = 13.2.
* Right Wall: 13.2.
* Top Wall: 16.8.
* Bottom Wall: 12.4.
* This creates a contradiction if it's a simple rectilinear polygon unless there are more sides.
* Ah, I see the inner corner.
* Left side consists of two segments: Top part 8.1, Bottom part 5.1.
* Bottom side is 12.4.
* Top side is 16.8.
* Right side is 13.2.
* This implies the shape is a large rectangle $16.8 \times 13.2$ with a piece missing?
* Missing piece dimensions:
* Width: $16.8 - 12.4 = 4.4 \text{ ft}$.
* Height: $13.2 - 8.1 = 5.1 \text{ ft}$? Or is the 8.1 the top part?
* Let's assume the 8.1 is the top-left vertical segment. And 5.1 is the bottom-left vertical segment.
* If the left side is straight, it would be one line. It is drawn as two lines meeting at a corner? No, it's drawn as a single vertical line with labels. Wait, looking at crop 4, the left side has a "step". It goes down 8.1, then steps IN? No, it steps RIGHT?
* The diagram shows the left boundary is NOT a straight line. It goes down 8.1, then right, then down 5.1? No, that would make it a Z shape.
* Standard L-shape: One long vertical back, one long horizontal base.
* Here, the "Back" is on the Left? No, the longest vertical is on the Right (13.2). The longest horizontal is on the Top (16.8).
* So it's an upside-down L rotated?
* Let's trace: Start Top-Left. Go Right 16.8. Go Down 13.2. Go Left (unknown). Go Up (unknown). Go Left (unknown). Go Up (unknown).
* Labels:
* Top: 16.8
* Right: 13.2
* Bottom: 12.4 (This is likely the bottom-most horizontal segment).
* Left-Bottom: 5.1 (Vertical).
* Left-Top: 8.1 (Vertical).
* This implies there is a horizontal segment connecting the 8.1 and 5.1 verticals? Yes, the "inner corner".
* So, Width of that inner horizontal segment = Total Top (16.8) - Bottom (12.4) = 4.4 ft.
* Let's calculate Area by splitting into two rectangles:
1. Bottom-Left Rectangle: Width 12.4, Height 5.1. Area = $12.4 \times 5.1 = 63.24$.
2. Top Rectangle: Spans the full width 16.8. Height is the remaining vertical part. Total Right Height is 13.2. Bottom Left Height is 5.1. So Top Height = $13.2 - 5.1 = 8.1$. This matches the label "8.1 ft". Perfect.
3. Area of Top Rectangle = $16.8 \times 8.1 = 136.08$.
4. Total Area: $63.24 + 136.08 = 199.32 \text{ ft}^2$.

Step 2: Find the Perimeter
Sum of all outer sides.
* Top: 16.8
* Right: 13.2
* Bottom: 12.4
* Left-Bottom Vertical: 5.1
* Inner Horizontal: $16.8 - 12.4 = 4.4$
* Left-Top Vertical: 8.1
* Sum: $16.8 + 13.2 + 12.4 + 5.1 + 4.4 + 8.1 = 60.0 \text{ ft}$.

Problem 5

Shape: T-shape on its side? Or a stepped shape.
Dimensions: Left 4.8 in, Bottom 15.2 in, Right 17.8 in, Top-Right 5.7 in, Inner-Top 6.5 in.

Step 1: Find the Area
Let's split it into two rectangles vertically.
* Right Rectangle: Width 5.7 in. Height 17.8 in.
* Area = $5.7 \times 17.8 = 101.46 \text{ in}^2$.
* Left Rectangle:
* Height is given as 4.8 in.
* Width? Total bottom is 15.2. Right part is 5.7. So Left Width = $15.2 - 5.7 = 9.5 \text{ in}$.
* Area = $9.5 \times 4.8 = 45.6 \text{ in}^2$.
* Total Area: $101.46 + 45.6 = 147.06 \text{ in}^2$.

*Check:* Does the top dimension match?
Top-Right is 5.7. Inner-Top is 6.5.
If Left Width is 9.5, and Inner-Top is 6.5, there is a discrepancy.
Let's look at the labels again.
"6.5 in" is labeling the horizontal segment of the "step" on the top left.
"5.7 in" is the top width of the right tower.
"15.2 in" is the total bottom width.
So, Left Width = $15.2 - 5.7 = 9.5 \text{ in}$.
The top of the left block is not fully exposed. The label "6.5 in" is on the horizontal surface.
This implies the left block might be narrower than the calculation? Or maybe the 6.5 is just a part of it?
Usually, in these problems, if a dimension is given, it defines the geometry.
If the left block width is 9.5, why label 6.5?
Maybe the shape is different.
Let's try splitting horizontally.
* Bottom Rectangle: Height 4.8. Width 15.2. Area = $15.2 \times 4.8 = 72.96$.
* Top Rectangle:
* Height? Total Right Height is 17.8. Bottom Height is 4.8. Top Height = $17.8 - 4.8 = 13.0 \text{ in}$.
* Width? Label says 5.7 in.
* Area = $5.7 \times 13.0 = 74.1 \text{ in}^2$.
* Total Area: $72.96 + 74.1 = 147.06 \text{ in}^2$.
This matches the previous calculation perfectly. The "6.5 in" label might be redundant or referring to something else, or perhaps I misinterpreted the left width.
Wait, if Top Height is 13, and Left Height is 4.8...
Let's check the horizontal lengths on top.
Total Width = 15.2.
Right Tower Width = 5.7.
Remaining Width = 9.5.
The label "6.5 in" is on the top of the left section.
Is it possible the left section doesn't go all the way to the edge? No, it's a solid polygon.
Perhaps the "6.5 in" is the width of the left part, and the "15.2" is the total?
If Left Width = 6.5, then Right Width = $15.2 - 6.5 = 8.7$.
But the label says Right Width = 5.7.
Contradiction: $6.5 + 5.7 = 12.2$, which is not 15.2.
There is a gap of $15.2 - 12.2 = 3.0 \text{ in}$.
Looking at the diagram, there is a vertical line dropping from the end of the 6.5 segment?
Ah, looking closely at Crop 5:
The shape has a left part (height 4.8), a middle part?
No, it looks like a standard L-tetris piece.
Left block: Height 4.8.
Right block: Height 17.8, Width 5.7.
Bottom total: 15.2.
This forces the Left Block Width to be $15.2 - 5.7 = 9.5$.
Why is "6.5 in" there?
It is labeling the horizontal segment *between* the left edge and the right tower?
Maybe the left block is actually composed of two parts?
Or maybe the 6.5 is the width of the left block, and the 15.2 includes an overhang?
Let's look at the vertices.
Top-Left corner. Go Right 6.5? Then Down? Then Right?
If I go Right 6.5, then Down, then Right to meet the tower...
If Left Width is 6.5, and Right Width is 5.7, Total Width = $6.5 + 5.7 = 12.2$.
But Bottom is 15.2.
This means there is a $15.2 - 12.2 = 3.0$ inch section unaccounted for.
Looking at the drawing, the left block (height 4.8) seems to extend further right than the top block (width 6.5?).
Yes! The label 6.5 is on the TOP of the left protrusion. The label 4.8 is the HEIGHT of the left protrusion.
The bottom label 15.2 is the TOTAL width.
The right label 5.7 is the WIDTH of the right tower.
The right height 17.8 is TOTAL height.
So, the left "block" is not a simple rectangle aligned with the top.
Actually, it looks like the left part has a "step" too?
No, simpler explanation: The label 6.5 is just the width of the top-left segment. The vertical line below it drops down to the main body.
Let's assume the shape is:
1. Right Tower: $5.7 \text{ wide} \times 17.8 \text{ high}$.
2. Left Wing: Attached to the side.
* Total Width 15.2. Right is 5.7. So Left Wing Width = 9.5.
* Height of Left Wing = 4.8.
* Why label 6.5? Maybe the Left Wing is not a rectangle? Maybe it tapers? No, "irregular polygons" in this context usually mean rectilinear.
* Maybe the 6.5 is the distance from the left edge to the inner corner?
* If so, there is another horizontal segment of length $9.5 - 6.5 = 3.0$?
* Looking at the diagram, there is a vertical line segment between the 6.5 top edge and the 4.8 side edge? No.
* Let's look at the junction. The 6.5 line ends. Then a vertical line goes DOWN. Then a horizontal line goes RIGHT?
* If that's the case, the shape is more complex.
* However, usually, if a dimension like 15.2 is given for the bottom, and 5.7 for the top right, the difference (9.5) is the total width of the left section.
* If the top of the left section is 6.5, there must be a step.
* Let's assume there is a step on the left block too.
* Left Block Top Width: 6.5.
* Left Block Bottom Width: 9.5.
* This would imply a trapezoid or a step. Given the right angles, it's a step.
* So, Left Section consists of:
* Top Part: Width 6.5. Height?
* Bottom Part: Width 9.5. Height?
* This is getting complicated. Let's look at the most standard interpretation of such worksheets. Often, labels can be slightly ambiguous.
* Hypothesis A: The 6.5 is a typo for 9.5. Area = 147.06.
* Hypothesis B: The shape has a step on the left.
* Left side height 4.8.
* Top left width 6.5.
* Then it steps down? Or steps right?
* If it steps right, the height of that step isn't given.
* Hypothesis C: The 6.5 refers to the horizontal segment of the "notch" if we view it differently?
* Let's look at the "6.5 in" position again. It is above the left block.
* Let's look at the "4.8 in" position. It is the left vertical side.
* Let's look at the "15.2 in" position. Bottom.
* Let's look at the "5.7 in" position. Top of right tower.
* Let's look at the "17.8 in" position. Right side.
* There is a vertical line separating the left mass and right mass.
* If we assume the left mass is a rectangle of $9.5 \times 4.8$, the area is 147.06.
* If we assume the label 6.5 is correct, then the left mass is NOT a simple rectangle of width 9.5 at the top.
* Perhaps the left mass is a rectangle of width 6.5 and height 4.8, PLUS another rectangle?
* If Left Top Width = 6.5, and Total Left Width = 9.5, there is a 3.0 difference.
* Is there a vertical segment labeled? No.
* However, notice the vertex where the 6.5 ends. It goes DOWN. Then RIGHT to join the tower?
* If so, what is the height of that drop?
* We don't know.
* BUT, look at the alignment. The 4.8 is the full height of the left side.
* If the shape steps IN at the top, the height of the top part is unknown.
* WAIT. Look at the label "6.5 in". It is inside the shape? No, outside.
* Look at the label "4.8 in".
* Is it possible the 6.5 is the width of the LEFT PART, and the 5.7 is the width of the RIGHT PART, and the 15.2 is WRONG or refers to something else?
* $6.5 + 5.7 = 12.2$.
* If the bottom is 15.2, maybe the right part is wider at the bottom? No, it's a rectangle.
* Maybe the left part is wider at the bottom?
* If Left Top = 6.5, Left Bottom = 9.5 (derived from 15.2-5.7).
* Then the left shape is a trapezoid? No, rectilinear.
* So it must have a step.
* Where is the step?
* If the top is narrower (6.5) than the bottom (9.5), the step is on the bottom-right of the left block? i.e., it bulges out at the bottom?
* Diagram shows the left block as a simple rectangle.
* Most likely scenario: The 6.5 label is the width of the left rectangle, and the 15.2 label is the total width, implying the right rectangle's width is $15.2 - 6.5 = 8.7$. BUT the right rectangle is labeled 5.7.
* Alternative: The 5.7 is the width of the right rectangle, and the 6.5 is the width of the left rectangle, and the 15.2 is the total width including a gap? No.
* Let's trust the "Outer Boundary" labels (15.2, 17.8, 4.8) and the clear component label (5.7). The 6.5 might be the length of the segment *excluding* some overlap?
* Actually, let's look at the math for 147.06. It uses 15.2 and 5.7. It ignores 6.5.
* Let's try using 6.5 and 5.7. Total Width = 12.2. Ignore 15.2?
* Area = Left ($6.5 \times 4.8$) + Right ($5.7 \times 17.8$).
* Left Area = 31.2. Right Area = 101.46. Total = 132.66.
* Which is more likely? In worksheets, "15.2" is a very specific number. "6.5" is also specific.
* Let's look at the visual proportions.
* Left width (visual) vs Right width (visual). Left looks almost double the right.
* If Left=9.5 and Right=5.7, ratio is ~1.6.
* If Left=6.5 and Right=5.7, ratio is ~1.1.
* Visually, the left part is significantly wider. So 9.5 is more likely than 6.5.
* Therefore, the 6.5 label might be indicating the distance from the left edge to the *inner corner* of a notch? But there is no notch on the left.
* Wait! Look at the top of the left block. Is there a notch?
* No.
* Okay, I will proceed with the calculation based on the bounding box dimensions (15.2 total width) as they define the overall scale, assuming the 6.5 might be a distractor or I am misinterpreting a subtle feature not visible. HOWEVER, looking at similar problems online, sometimes the "inner" labels define the cutouts.
* Let's reconsider the shape. What if the 6.5 is the width of the *right* part of the left block?
* Let's stick to the most robust method: Decomposition into Rectangles using the clearest outer bounds.
* Rectangle 1 (Right): $5.7 \times 17.8$.
* Rectangle 2 (Left): Width $15.2 - 5.7 = 9.5$. Height 4.8.
* Area = 147.06.
* Perimeter:
* Bottom: 15.2
* Right: 17.8
* Top Right: 5.7
* Inner Vertical: $17.8 - 4.8 = 13.0$
* Top Left: 9.5 (Calculated) OR 6.5 (Given)? If we use 6.5, we have a mismatch.
* If we assume the top left is 6.5, then there is a step.
* Step Horizontal: $9.5 - 6.5 = 3.0$.
* Step Vertical: Unknown.
* This makes the problem unsolvable without more info.
* Therefore, the 6.5 MUST be the width of the left block, and the 15.2 is wrong? Or 5.7 is wrong?
* Let's check $6.5 + 5.7 = 12.2$. If Bottom is 15.2, maybe the right block is wider at the bottom? No.
* Maybe the left block is 6.5, and there is a 3.0 gap? No.
* Let's assume the label "6.5 in" is actually the height of the top part of the right tower? No, it's horizontal.
* Let's assume the label "15.2" is the perimeter? No, "in".
* Okay, I will provide the answer based on the consistent set: Left Width derived from Total Width. This is the standard way to solve these "missing side" problems. The 6.5 is likely an error in the problem sheet or refers to a sub-segment not clearly depicted as a step.
* *Self-Correction*: What if the 6.5 is the width of the left part, and the 5.7 is the width of the right part, and the 15.2 is the sum of the bottom of the left part and the bottom of the right part? Yes.
* If Left Top is 6.5, and it's a rectangle, Left Bottom is 6.5.
* Then Right Bottom is $15.2 - 6.5 = 8.7$.
* But Right Top is 5.7.
* Then the Right part is a trapezoid? No.
* I will bet on Area = 147.06 sq in and Perimeter = 55.4 in (using calculated widths).
* Perimeter Calculation:
* Bottom: 15.2
* Right: 17.8
* Top Right: 5.7
* Inner Vertical: 13.0
* Top Left: 9.5
* Left: 4.8
* Sum: $15.2 + 17.8 + 5.7 + 13.0 + 9.5 + 4.8 = 66.0 \text{ in}$.

Problem 6

Shape: L-shape.
Dimensions: Top 18.8 ft, Right 25.5 ft, Left Top 5.5 ft, Inner Horizontal 4.2 ft.

Step 1: Find the Area
Split into two rectangles.
* Top Rectangle: Height 5.5 ft. Width 18.8 ft.
* Area = $18.8 \times 5.5 = 103.4 \text{ ft}^2$.
* Bottom Rectangle:
* Width? The inner horizontal label is 4.2 ft. This usually indicates the width of the vertical leg sticking down.
* Let's verify. If the right leg width is 4.2, then the left part of the top bar is $18.8 - 4.2 = 14.6$.
* Height of Bottom Rectangle? Total Right Height is 25.5. Top Height is 5.5. So Bottom Height = $25.5 - 5.5 = 20.0 \text{ ft}$.
* Area = $4.2 \times 20.0 = 84.0 \text{ ft}^2$.
* Total Area: $103.4 + 84.0 = 187.4 \text{ ft}^2$.

Step 2: Find the Perimeter
* Top: 18.8
* Right: 25.5
* Bottom: 4.2 (Width of the leg)
* Inner Vertical: 20.0
* Inner Horizontal: $18.8 - 4.2 = 14.6$
* Left: 5.5
* Sum: $18.8 + 25.5 + 4.2 + 20.0 + 14.6 + 5.5 = 88.6 \text{ ft}$.

Problem 7

Shape: U-shape or C-shape?
Dimensions: Top 9 cm, Right Top 6.8 cm, Inner Horizontal 5.5 cm, Right Bottom 6.8 cm, Left 16 cm.

Step 1: Find the Area
Imagine a big rectangle minus the empty space.
* Total Width: 9 cm.
* Total Height: 16 cm.
* Area of Big Rectangle: $9 \times 16 = 144 \text{ cm}^2$.
* Empty Space (Notch):
* Width: 5.5 cm.
* Height? Total Height 16. Top arm 6.8. Bottom arm 6.8.
* Notch Height = $16 - 6.8 - 6.8 = 2.4 \text{ cm}$.
* Area of Notch = $5.5 \times 2.4 = 13.2 \text{ cm}^2$.
* Total Area: $144 - 13.2 = 130.8 \text{ cm}^2$.

Step 2: Find the Perimeter
Add all outer edges plus the inner notch edges.
* Left: 16
* Top: 9
* Right Top: 6.8
* Notch Top Horizontal: 5.5
* Notch Vertical: 2.4
* Notch Bottom Horizontal: 5.5
* Right Bottom: 6.8
* Bottom: 9
* Sum: $16 + 9 + 6.8 + 5.5 + 2.4 + 5.5 + 6.8 + 9 = 61.0 \text{ cm}$.

Problem 8

Shape: H-shape or I-beam shape.
Dimensions: Left 16.8 m, Top Left 3.8 m, Inner Vertical 4.4 m, Inner Horizontal 8.8 m, Top Right 3.8 m.

Step 1: Find the Area
Split into three vertical rectangles (Left, Middle, Right)? Or Top, Middle, Bottom?
Let's split into Left, Right, and Center.
* Left Rectangle: Width 3.8 m. Height 16.8 m.
* Area = $3.8 \times 16.8 = 63.84 \text{ m}^2$.
* Right Rectangle: Width 3.8 m. Height 16.8 m.
* Area = $3.8 \times 16.8 = 63.84 \text{ m}^2$.
* Middle Rectangle:
* Width: 8.8 m.
* Height? The label "4.4 m" is on the vertical segment of the cutout.
* This implies the "arms" of the H have a certain thickness.
* Total Height 16.8. The cutout height is 4.4?
* Usually, the "4.4 m" label on the vertical inner edge indicates the height of the gap.
* So, Height of Middle Connector = Total Height - Gap? No, the middle part IS the connector.
* If the gap is 4.4 high, then the middle rectangle height is... wait.
* The label 4.4 is on the vertical edge of the *empty space*.
* So the empty space height is 4.4?
* If so, the solid middle part height is $16.8 - 4.4 - 4.4$? No, that assumes symmetry.
* Let's look at the label placement. "4.4 m" is next to the top inner vertical edge.
* This means the top arm has a height of 4.4 m?
* If Top Arm Height = 4.4, and Bottom Arm Height = 4.4 (symmetry assumed), then Middle Height = $16.8 - 4.4 - 4.4 = 8.0 \text{ m}$.
* Area of Middle = $8.8 \times 8.0 = 70.4 \text{ m}^2$.
* Total Area = $63.84 + 63.84 + 70.4 = 198.08 \text{ m}^2$.

*Alternative Interpretation:*
Maybe the 4.4 is the height of the middle bar?
If Middle Height = 4.4, then Arms