This worksheet challenges students to calculate the area and perimeter for six distinct compound shapes, utilizing mixed units like meters, feet, and kilometers.

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

1) Rectangle and Quarter Circle

This shape is made of a rectangle at the bottom and a quarter-circle on top left.
* Rectangle: Length = $22.2\text{ in}$, Width = $11.5\text{ in}$.
* Quarter Circle Radius ($r$): The total height on the left is not given directly, but we can find the radius. The top part is a quarter circle. The horizontal side $ED$ is part of the rectangle's top. Wait, looking at the diagram, the shape is a rectangle $ABCD$ with a quarter circle attached to side $AD$? No, it looks like a rectangle $ABCE$ (if we extend lines) or simply a rectangle plus a quarter circle.
* Let's look at the dimensions. Bottom $AB = 22.2$. Left side $AF = 11.5$. Top right vertical side $BC$ is part of the rectangle. The curve is from $F$ to $E$. The center of the circle is likely at the corner above $A$. Let's assume the rectangle is the main body and the quarter circle sits on top of the left side?
* Actually, let's look closer. It looks like a rectangle with width $22.2$ and height $11.5$, and a quarter circle attached to the top-left corner? No, the arc connects $F$ and $E$. $F$ is above $A$. $E$ is to the right of $F$. The segment $FE$ is an arc. The segment $ED$ is horizontal. The segment $DC$ is vertical.
* Let's re-read the diagram.
* Rectangle part: Base $AB = 22.2$. Height $BC$? We see $DC = 10.1$. We see $AF = 11.5$.
* The shape seems to be composed of a rectangle at the bottom and a quarter circle on the top left.
* Let's assume the "center" of the quarter circle is the point directly above $A$ at the same level as $D$? No.
* Standard interpretation: This is a rectangle with a quarter-circle cut out or added? It looks added.
* Let's look at the coordinates/lengths.
* Vertical side on left: $A$ to $F$ is $11.5$.
* Horizontal side on top right: $E$ to $D$ is unknown? No, $D$ to $C$ is $10.1$.
* There is a right angle at $D$. So $ED$ is horizontal.
* There is a right angle at the corner near $F$? No, $F$ is on the arc.
* Let's assume the shape is a rectangle of width $22.2$ and height $11.5$ (left side) + something?
* Actually, usually these problems combine simple shapes.
* Shape = Rectangle + Quarter Circle.
* Rectangle dimensions: Width $22.2$. Height? The right side has a segment $DC = 10.1$. The left side has $AF = 11.5$. This implies the rectangle isn't uniform height or there's a step.
* Let's look at the quarter circle. The radius is usually one of the side lengths.
* If the center is at the intersection of the vertical line up from $A$ and the horizontal line from $D$... let's call that point $O$. Then $OF$ is radius and $OE$ is radius.
* If $AF = 11.5$ and $DC = 10.1$, and the base is $22.2$.
* Let's assume the rectangle is the bottom part with height $10.1$ (matching $DC$). Then the left side would be $10.1$. But $AF$ is $11.5$. This means the part above the rectangle on the left is $11.5 - 10.1 = 1.4$? That doesn't seem right for a quarter circle radius.
* Alternative interpretation: The shape is a large rectangle minus a piece? Or a rectangle plus a quarter circle on top?
* Let's look at Problem 1 again carefully.
* Points: $A$ (bottom left), $B$ (bottom right), $C$ (mid right), $D$ (top right of rect part), $E$ (start of arc), $F$ (end of arc/top left).
* $AB = 22.2$. $BC$ is vertical? No, $C$ is a corner. $DC$ is vertical, length $10.1$. $CB$ is vertical? The line goes from $C$ down to $B$? Yes, implied rectangle corner. So height of right side is $10.1$.
* Left side $AF = 11.5$.
* Top part is a quarter circle connecting $F$ and $E$.
* For $FE$ to be a quarter circle, the center must be at the corner formed by extending $AF$ up and $DE$ left? Or extending $DE$ left and $AF$ up?
* Let's assume the center is at the top-left corner of the "bounding box".
* If the center is at $(0, H)$, and the arc goes from $(0, H-r)$ to $(r, H)$.
* Here, $F$ is at top left? No, $F$ is labeled on the vertical segment.
* Let's try this: The shape consists of a rectangle ($22.2 \times 10.1$) and a quarter circle on top of the left side?
* If the rectangle height is $10.1$, then the left side of the rectangle is $10.1$. The total left side is $11.5$. So the extra bit is $1.4$. This doesn't match a clean radius.
* Let's try: The shape is a rectangle ($22.2 \times 11.5$) with a bite taken out? No.
* Let's look at the radius label. There is no explicit radius label.
* However, notice $ED$ is horizontal. $DC$ is vertical.
* Usually, in these diagrams, if it's a quarter circle, the radius equals the adjacent straight sides if they form a square corner.
* Let's assume the center of the circle is the point $P$ such that $PF$ and $PE$ are radii.
* If we drop a perpendicular from $E$ to the left side, and from $F$ to the top...
* Let's assume the standard case: The shape is a rectangle with a quarter circle attached.
* Width of rectangle = $22.2$. Height of right side = $10.1$.
* Height of left side = $11.5$.
* This implies the "base" rectangle has height $10.1$. The left side sticks up $1.4$ higher? No, that's weird.
* Maybe the radius is $11.5 - 10.1 = 1.4$? Unlikely.
* Maybe the radius is determined by the horizontal distance?
* Let's look at the horizontal segments. $AB = 22.2$. $ED$ is part of the top.
* If the quarter circle is on the top left, its radius $r$ would define the position of $E$.
* Distance from left edge to $E$ is $r$.
* Distance from top of left edge ($F$) to center?
* Let's assume the center is at the top-left corner of the rectangular block defined by height $11.5$? No.
* Let's assume the center is at the vertex where the vertical line $AF$ meets the horizontal line $DE$ if extended?
* Let's guess the radius is the difference in heights? $11.5 - 10.1 = 1.4$? No.
* Let's look at similar problems online. Often, the radius is given or obvious.
* Is it possible $AF$ is the radius? If $r=11.5$, then the center is at $A$? No, arc is at top.
* Is it possible the vertical side $11.5$ includes the radius?
* Let's assume the shape is a rectangle of $22.2 \times 10.1$ PLUS a quarter circle of radius $r$ sitting on top of the left side?
* If so, the total height on left is $10.1 + r = 11.5 \Rightarrow r = 1.4$.
* Then the area would be Area(Rect) + Area(QC).
* Perimeter would be $AB + BC + CD + \text{Arc} + FA$? No, $FA$ is internal? No, $F$ is top point.
* Perimeter path: $A \rightarrow B \rightarrow C \rightarrow D \rightarrow E (\text{arc}) \rightarrow F \rightarrow A$.
* If $r=1.4$:
* Area Rect = $22.2 \times 10.1 = 224.22$.
* Area QC = $\frac{1}{4} \pi (1.4)^2 \approx 1.54$.
* Total Area $\approx 225.76$.
* Perimeter: $AB(22.2) + BC(10.1) + CD(10.1 \text{ wait, } DC=10.1 \text{ is vertical}) + DE(\text{horizontal}) + \text{Arc} + FA(11.5)$?
* Wait, $D$ to $C$ is $10.1$. $C$ to $B$ is vertical? The diagram shows $C$ connected to $B$. So $CB$ is vertical. Since $AB$ is horizontal and angles are right, $CB$ height should match the rectangle height. If the rectangle height is $10.1$, then $CB=10.1$.
* $DE$ length: Total width $22.2$. Radius is $1.4$. So $DE = 22.2 - 1.4 = 20.8$.
* Arc length: $\frac{1}{4} \times 2 \pi (1.4) \approx 2.20$.
* Perimeter: $22.2 (AB) + 10.1 (BC) + 10.1 (CD? \text{No, } DC \text{ is vertical}) + 20.8 (DE) + 2.20 (\text{Arc}) + 11.5 (FA)$?
* Wait, the boundary is $A-B-C-D-E-F-A$.
* $A \rightarrow B$: $22.2$.
* $B \rightarrow C$: Vertical up. Length $10.1$.
* $C \rightarrow D$: Horizontal left? No, $D$ is above $C$? Diagram shows $D$ to the left of $C$? No, $D$ is a corner. $C$ is a corner. $DC$ is a vertical segment of length $10.1$. So $D$ is top-right of the lower block?
* Let's re-examine diagram 1.
* $A$ (bottom left), $B$ (bottom right). Line $AB$ is bottom.
* $B$ to $C$ is vertical? The label $10.1$ is next to the vertical segment ending at $D$? No, the label $10.1$ is next to the vertical segment $DC$? Or is $DC$ horizontal?
* Usually letters go in order around perimeter. $A-B-C-D-E-F$.
* $AB$ = bottom.
* $BC$ = right side vertical?
* $CD$ = top right horizontal?
* $DE$ = ?
* Let's look at the labels again.
* Left side: $A$ to $F$ is $11.5$.
* Bottom: $A$ to $B$ is $22.2$.
* Right side structure: There is a vertical line segment labeled $10.1$. It connects to $D$. And $D$ connects to $C$?
* Actually, it looks like a rectangle $ABXD$ where $X$ is below $D$?
* Let's assume the standard "L-shape with a curve" or "Rectangle + Semicircle/Quartercircle".
* Given the ambiguity and small numbers, let's look at Problem 2 which is clearer.

2) Rectangle and Semicircle

* Shape: A rectangle with a semicircle on top.
* Dimensions:
* Rectangle Width ($AB$) = Diameter of semicircle = $29.2\text{ mm}$.
* Rectangle Height ($AD$ or $BC$) = $3.1\text{ mm}$.
* Area:
* Area of Rectangle = $\text{Width} \times \text{Height} = 29.2 \times 3.1$.
* Area of Semicircle = $\frac{1}{2} \pi r^2$. Radius $r = \frac{29.2}{2} = 14.6\text{ mm}$.
* Total Area = Area(Rect) + Area(Semi).
* Perimeter:
* The perimeter includes the three sides of the rectangle (Bottom, Left, Right) and the curved arc of the semicircle. The top side of the rectangle is inside the shape.
* Perimeter = $AB + AD + BC + \text{Arc}$.
* Arc Length = $\frac{1}{2} \times \pi \times d = \frac{1}{2} \times \pi \times 29.2$.

Calculations for #2:
* Area:
* Rect: $29.2 \times 3.1 = 90.52\text{ mm}^2$.
* Semi: $r = 14.6$. $r^2 = 213.16$.
* Area Semi = $0.5 \times \pi \times 213.16 \approx 0.5 \times 3.14159 \times 213.16 \approx 334.83\text{ mm}^2$.
* Total Area = $90.52 + 334.83 = 425.35\text{ mm}^2$.
* Perimeter:
* Straight sides: $29.2 (\text{bottom}) + 3.1 (\text{left}) + 3.1 (\text{right}) = 35.4\text{ mm}$.
* Arc: $0.5 \times \pi \times 29.2 = 14.6 \pi \approx 45.87\text{ mm}$.
* Total Perimeter = $35.4 + 45.87 = 81.27\text{ mm}$.

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3) Rectangle and Triangle

* Shape: A rectangle on the left and a triangle on the right.
* Dimensions:
* Rectangle: Height $AF = 11.1\text{ cm}$, Width $FD = 11.1\text{ cm}$? Wait, $FD$ is top side. $AB$ is bottom.
* Label $11.1\text{ cm}$ is on top side $FD$? No, $F$ to $D$ is labeled $11.1$.
* Label $11.1\text{ cm}$ is on left side $AF$? Yes.
* So the left part is a square $11.1 \times 11.1$.
* Triangle: Attached to the right side of the square.
* Base of triangle (vertical side shared with square) = $11.1\text{ cm}$.
* Height of triangle (horizontal distance from base to tip $C$) = Label says $12.1\text{ cm}$? No, the label $12.1\text{ cm}$ is on the slanted side $DC$? Or is it the horizontal height?
* Looking at the dashed line: There is a dashed horizontal line from the midpoint? No, from the corner $D$?
* There is a dimension $14.4\text{ cm}$ pointing to the dashed line. The dashed line goes from the vertical side to the tip $C$. This represents the height of the triangle.
* There is a dimension $12.1\text{ cm}$ on the bottom slanted side $BC$? Or is it the vertical drop?
* Let's look closely at crop 3.
* Square part: Side $11.1$.
* Triangle part: Tip $C$.
* Dashed line indicates height of triangle = $14.4\text{ cm}$.
* Side $DC$ is labeled $12.1\text{ cm}$.
* Side $BC$ is labeled $12.1\text{ cm}$.
* So it's an isosceles triangle attached to the square.
* Area:
* Area of Square = $11.1 \times 11.1$.
* Area of Triangle = $\frac{1}{2} \times \text{Base} \times \text{Height}$.
* Base = Side of square = $11.1\text{ cm}$.
* Height = $14.4\text{ cm}$.
* Perimeter:
* Outer boundary: $AF + AB + BC + CD + DF$? No, $DF$ is internal? No, $D$ and $F$ are corners of the square. The perimeter is $A \rightarrow F \rightarrow D \rightarrow C \rightarrow B \rightarrow A$.
* Sides: $AF (11.1) + FD (11.1) + DC (12.1) + CB (12.1) + BA (11.1)$.
* Note: $AB$ is the bottom of the square.

Calculations for #3:
* Area:
* Square: $11.1^2 = 123.21\text{ cm}^2$.
* Triangle: $0.5 \times 11.1 \times 14.4 = 0.5 \times 159.84 = 79.92\text{ cm}^2$.
* Total Area = $123.21 + 79.92 = 203.13\text{ cm}^2$.
* Perimeter:
* Sum of outer sides: $11.1 (AF) + 11.1 (FD) + 12.1 (DC) + 12.1 (CB) + 11.1 (BA)$.
* Total = $11.1 + 11.1 + 12.1 + 12.1 + 11.1 = 57.5\text{ cm}$.

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4) Rectangle and Two Triangles (Trapezoid-like ends?)

* Shape: A central rectangle with two triangles on the sides? Or a large rectangle with triangles cut out?
* Looking at the vertices: $A, B$ at bottom. $F, E$ at top.
* Left side: Indented triangle $H-G-?$? No, points are $A, H, G, F$?
* Let's trace the perimeter: $A \rightarrow H \rightarrow G \dots$?
* Labels:
* Top side $FE = 20.1\text{ ft}$.
* Left side structure: Vertical drop from $F$ is $3.1\text{ ft}$? No, label $3.1$ is near the top left corner.
* Label $4.1\text{ ft}$ is the vertical height of the bottom section?
* Label $3.0\text{ ft}$ is the horizontal depth of the cutout?
* Label $4.1\text{ ft}$ is on the right side too.
* Label $3.1\text{ ft}$ is on the right side top.
* It looks like a rectangle of width $20.1$ and height $(4.1 + 3.1) = 7.2$?
* With triangular "bites" taken out of the left and right sides?
* Let's check the shape. It looks like a hexagon $A-B-C-D-E-F$? No.
* Vertices: $A$ (bottom left), $B$ (bottom right).
* Right side: Goes up from $B$ to $C$? No, $B$ to some point, then in to $C$?
* Let's look at the dashed line. It spans the width $20.1$.
* The shape is symmetric.
* Central Rectangle part: Height is determined by the vertical segments labeled $4.1$? No, $4.1$ is the vertical leg of the triangle?
* Let's decompose it into a central rectangle and two triangles on the ends?
* Actually, it looks like a rectangle with two triangles removed from the sides.
* Total Width = $20.1$.
* Total Height = $4.1 + 3.1 = 7.2\text{ ft}$.
* The "cuts" are triangles.
* Left Cut: Base is the vertical side of height $?$. Depth is $3.0$.
* Let's look at the labels again.
* Left side: Top segment vertical is $3.1$. Bottom segment vertical is $4.1$. The gap between them is the base of the indented triangle.
* Wait, the dashed line is in the middle.
* The label $3.0\text{ ft}$ is the horizontal distance from the outer edge to the inner vertex $G$ (left) and $C$ (right)?
* Let's assume the shape is a large rectangle $20.1 \times 7.2$ MINUS two triangles.
* Triangle dimensions:
* Height (horizontal depth) = $3.0\text{ ft}$.
* Base (vertical span): The total height is $7.2$. The top straight part is $3.1$? No, $3.1$ is labeled on the top right vertical segment. $4.1$ is labeled on the bottom right vertical segment.
* So the vertical gap for the triangle base = Total Height - Top Part - Bottom Part?
* $7.2 - 3.1 - 4.1 = 0$? That means the triangles touch the top and bottom?
* If Top Part is $3.1$ and Bottom Part is $4.1$, sum is $7.2$. This implies the "indentation" starts immediately from the corners?
* No, looking at the diagram, there are vertical segments.
* Left side: Top vertical segment $F$ down to start of slope? Label $3.1$ is there.
* Bottom vertical segment $A$ up to start of slope? Label $4.1$ is there.
* So the base of the indented triangle is the remaining vertical space?
* But $3.1 + 4.1 = 7.2$. If total height is $7.2$, there is no space left for a vertical base.
* This implies the vertices of the indentation are the corners themselves? i.e., The side is just a zig-zag $F \rightarrow G \rightarrow A$?
* If so, the shape is defined by vertices $F, G, A, B, C, E$.
* Let's check the horizontal positions.
* Width $FE = 20.1$.
* Depth of $G$ and $C$ is $3.0$ from the side.
* So, Area = Area of bounding box - Area of two triangles?
* Bounding Box: Width $20.1$, Height $7.2$.
* Triangle 1 (Left): Base is vertical side $FA$? No, $F$ and $A$ are corners. The "base" of the removed triangle would be the segment connecting $F$ and $A$ if it were straight. But it's not.
* Actually, simpler view: The shape is composed of a central rectangle and two trapezoids? Or just calculate by subtraction.
* Area = (Area of Rectangle $20.1 \times 7.2$) - (Area of Left Triangle) - (Area of Right Triangle).
* Left Triangle: Base = Vertical distance between $F$ and $A$? No, $F$ and $A$ are the endpoints. The "base" of the removed triangle lies on the vertical line connecting $F$ and $A$. Length = $7.2$. Height = $3.0$.
* Wait, if the base is $7.2$, then the vertical segments labeled $3.1$ and $4.1$ wouldn't exist as straight vertical edges. They would be part of the triangle base.
* BUT the diagram shows vertical lines labeled $3.1$ and $4.1$. This means the indentation does NOT span the whole height.
* Contradiction: $3.1 + 4.1 = 7.2$. If the total height is $7.2$, and the top and bottom segments take up all the height, the "middle" segment for the triangle base has length $0$.
* Re-reading labels:
* Maybe $3.1$ is the height of the top part, and $4.1$ is the height of the bottom part, and there is a middle part?
* Or maybe $3.1$ and $4.1$ are the lengths of the slanted sides? No, they are next to vertical lines.
* Let's look at the right side. Top vertical segment $3.1$. Bottom vertical segment $4.1$.
* Is it possible the total height is NOT $7.2$?
* Maybe the $3.1$ and $4.1$ overlap? No.
* Maybe the label $3.0$ is not the depth?
* Let's look at the dashed line. It connects the inner vertices.
* Let's assume the standard interpretation: The shape is a rectangle with two triangular notches.
* If the notches don't span the full height, there must be a middle vertical segment. But there isn't one drawn.
* Alternative: The labels $3.1$ and $4.1$ refer to the vertical positions of the vertices?
* Let's assume the vertices are:
* Top-Left $F$.
* Inner-Left $G$.
* Bottom-Left $A$.
* The segment $FG$ is slanted? No, $F$ to some point is vertical?
* Diagram shows: From $F$, go down vertically (length $3.1$?). Then go diagonally to $G$? Then diagonally to $A$?
* No, it looks like $F \rightarrow$ (down) $\rightarrow$ (diagonal in) $\rightarrow G \rightarrow$ (diagonal out) $\rightarrow$ (down) $\rightarrow A$?
* Let's count segments on left:
1. Vertical down from $F$.
2. Diagonal to $G$.
3. Diagonal to ...?
* Actually, it looks like a single "V" cut. $F \rightarrow G \rightarrow A$.
* If it is $F \rightarrow G \rightarrow A$, then the vertical distance $F$ to $A$ is the sum of the vertical components of $FG$ and $GA$.
* If the cut is symmetric, and the total height is $H$.
* Why are there labels $3.1$ and $4.1$?
* Maybe $3.1$ is the vertical leg of the top triangle and $4.1$ is the vertical leg of the bottom triangle?
* If so, Total Height = $3.1 + 4.1 = 7.2$.
* And the horizontal depth is $3.0$.
* So, Area = Area of Rectangle ($20.1 \times 7.2$) MINUS Area of two triangles (Left and Right).
* Left Triangle Base (vertical) = $7.2$? No, the triangle is formed by the points $F, A$ and the inner point $G$?
* If the boundary is $F-G-A$, then the "removed" part is a triangle with base $FA$ (vertical, length $7.2$) and height $3.0$ (horizontal).
* Area Removed (Left) = $0.5 \times 7.2 \times 3.0 = 10.8$.
* Area Removed (Right) = $0.5 \times 7.2 \times 3.0 = 10.8$.
* Total Area = $(20.1 \times 7.2) - 10.8 - 10.8$.
* $20.1 \times 7.2 = 144.72$.
* $144.72 - 21.6 = 123.12\text{ sq ft}$.
* Let's check Perimeter.
* Perimeter = Top ($20.1$) + Bottom ($20.1$) + Left Slants ($FG + GA$) + Right Slants ($EC + CB$).
* We need the lengths of the slants.
* Left Slants: The triangle has height $3.0$ and base $7.2$. Is it isosceles?
* The diagram doesn't specify where $G$ is vertically.
* However, the labels $3.1$ and $4.1$ suggest asymmetry or specific segment lengths.
* If the vertical segments labeled $3.1$ and $4.1$ ARE the vertical projections of the slanted lines?
* i.e., Vertical drop of top slant = $3.1$. Vertical rise of bottom slant = $4.1$.
* Then Left Side consists of two segments:
1. Top slant: $\Delta y = 3.1$, $\Delta x = 3.0$. Length = $\sqrt{3.1^2 + 3.0^2}$.
2. Bottom slant: $\Delta y = 4.1$, $\Delta x = 3.0$. Length = $\sqrt{4.1^2 + 3.0^2}$.
* This fits the visual of a "notch" that doesn't necessarily hit the midline.
* So, Perimeter Left = $\sqrt{3.1^2 + 3.0^2} + \sqrt{4.1^2 + 3.0^2}$.
* Perimeter Right = Same (symmetric).
* Top = $20.1$. Bottom = $20.1$.
* Total Perimeter = $20.1 + 20.1 + 2 \times (\text{Left Slants})$.

Calculations for #4:
* Area:
* Method: Subtraction from bounding box.
* Bounding Box Width = $20.1$. Height = $3.1 + 4.1 = 7.2$.
* Area Box = $20.1 \times 7.2 = 144.72\text{ ft}^2$.
* Removed Area (Left): Triangle with base $7.2$ (vertical) and height $3.0$ (horizontal). Area = $0.5 \times 7.2 \times 3.0 = 10.8\text{ ft}^2$.
* Removed Area (Right): Same = $10.8\text{ ft}^2$.
* Total Area = $144.72 - 10.8 - 10.8 = 123.12\text{ ft}^2$.
* Perimeter:
* Top + Bottom = $20.1 + 20.1 = 40.2\text{ ft}$.
* Left Side Lengths:
* Top Slant: $\sqrt{3.1^2 + 3.0^2} = \sqrt{9.61 + 9.00} = \sqrt{18.61} \approx 4.314\text{ ft}$.
* Bottom Slant: $\sqrt{4.1^2 + 3.0^2} = \sqrt{16.81 + 9.00} = \sqrt{25.81} \approx 5.080\text{ ft}$.
* Total Left = $4.314 + 5.080 = 9.394\text{ ft}$.
* Right Side Lengths: Same as Left = $9.394\text{ ft}$.
* Total Perimeter = $40.2 + 9.394 + 9.394 = 58.988 \approx 58.99\text{ ft}$.

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5) Complex Polygon (Trapezoids/Triangles)

* Shape: Looks like a central rectangle/trapezoid with triangles on ends?
* Let's break it down.
* Top side $ED = 18.1\text{ km}$.
* Left side structure: $E$ to $F$? No, $E$ is top left?
* Vertices: $E$ (top left), $D$ (top right).
* $D$ to $C$? $C$ is bottom right?
* Let's trace: $E-D-C-B-A-F-E$?
* Labels:
* Top $ED = 18.1$.
* Right side: Vertical drop $11.1$? No, label $11.1$ is on the slanted side $DC$? Or vertical?
* There is a dashed line dropping from $D$ to $B$? Length $9.3$?
* There is a dashed line dropping from $E$ to $F$? No, $F$ is bottom left.
* Let's look at the "heights".
* Right side: Vertical segment labeled $9.3\text{ km}$? It's a dashed line. It represents the height of the right trapezoid/triangle part.
* Left side: Vertical segment labeled $9.0\text{ km}$? Dashed line.
* Bottom structure:
* Point $A$ is the bottom tip.
* $F$ to $G$? $G$ is on the bottom left?
* Labels on bottom left: $4.3\text{ km}$ (horizontal?), $12.1\text{ km}$ (slanted?).
* Labels on bottom right: $4.3\text{ km}$ (horizontal?), $12.1\text{ km}$ (slanted?).
* Center bottom: $A$ is tip.
* This shape looks like a central rectangle with two triangles on the bottom and two trapezoids on the sides?
* Let's try decomposition:
1. Central Rectangle:
* Width = Top side $ED = 18.1$?
* Wait, the side parts stick out?
* Let's look at the dashed lines.
* There is a rectangle in the middle?
* Vertices $E, D$ at top.
* Dashed lines go down from $E$ and $D$.
* Left dashed line length $9.0$. Right dashed line length $9.3$.
* This implies the shape is NOT a simple rectangle in the middle because heights differ.
* However, the top is flat ($ED$).
* The bottom is complex.
* Let's split into 3 vertical strips:
* Left Strip: A trapezoid or triangle?
* Top width? Unknown.
* Bottom width? $4.3$?
* Height? $9.0$?
* Slanted side $12.1$?
* Check Pythagoras: $\sqrt{9.0^2 + 4.3^2} = \sqrt{81 + 18.49} = \sqrt{99.49} \approx 9.97$. This is not $12.1$.
* So the $12.1$ side is not the hypotenuse of a right triangle with legs $9.0$ and $4.3$.
* Maybe $12.1$ is the slanted side $FA$?
* And $4.3$ is the horizontal distance from $F$ to the vertical line?
* Let's assume the shape is composed of:
* A central rectangle of width $W$ and height $H$?
* Two side trapezoids?
* A bottom triangle?
* Let's look at the labels again very carefully.
* Top: $18.1$.
* Right Side: Vertical dashed line $9.3$. Horizontal bottom part $4.3$. Slanted side $11.1$? No, $11.1$ is labeled on the upper slanted part?
* There is a label $11.1$ on the right upper slanted side $DC$?
* There is a label $11.1$ on the left upper slanted side $EF$?
* So, Top part is a trapezoid?
* Let's decompose horizontally:
* Top Part: An isosceles trapezoid?
* Top base $18.1$.
* Legs $11.1$.
* Height? Not given directly.
* Bottom Part:
* Triangle $ABC$?
* Height?
* Base?
* This is getting complicated. Let's try vertical decomposition again.
* Left Section:
* Top slanted side $11.1$.
* Bottom slanted side $12.1$.
* Horizontal width at bottom $4.3$?
* Vertical height of top part $9.0$? (Dashed line).
* If the left part is a polygon with vertices $E, F, A, \dots$
* Let's assume the dashed lines define a central rectangle.
* Central Rectangle Width = $18.1$? No, $18.1$ is the total top width.
* If the side pieces are attached to the sides of a central rectangle, then the top width of the central rectangle is less than $18.1$.
* But the lines $EF$ and $DC$ are slanted outward? Or inward?
* Diagram shows $E$ and $D$ are the widest points at the top? No, $F$ and $C$ are further out?
* Visually, $F$ is to the left of $E$. $C$ is to the right of $D$.
* So the shape widens towards the middle?
* Let's assume:
* Central Rectangle: Width $18.1$. Height?
* Left Wing: Attached to left side.
* Right Wing: Attached to right side.
* Bottom Tip: Attached to bottom.
* Actually, let's look at the dashed lines forming a rectangle in the middle.
* The dashed lines drop from $E$ and $D$.
* The distance between these dashed lines is likely the width of the central part.
* But $ED = 18.1$.
* The left wing has a horizontal span of $4.3$?
* The right wing has a horizontal span of $4.3$?
* If so, Total Width at bottom = $4.3 + 18.1 + 4.3 = 26.7$?
* But the bottom comes to a point $A$.
* Let's calculate Area by summing parts:
1. Central Rectangle:
* Width = $18.1$.
* Height = ? The dashed lines have lengths $9.0$ (left) and $9.3$ (right). This suggests the "shoulders" are at different heights. This makes a single central rectangle impossible unless the top is slanted, but $ED$ is horizontal.
* Contradiction: If $ED$ is horizontal and dashed lines are vertical, their lengths should be equal if they hit the same horizontal baseline. They hit different baselines?
* Left dashed line hits the line extending from $F$?
* Right dashed line hits the line extending from $C$?
* Let's assume the shape is symmetric despite the labels $9.0$ and $9.3$? $9.0$ vs $9.3$ is a big difference.
* Maybe $9.0$ is the height of the left trapezoid and $9.3$ is the height of the right trapezoid.
* Decomposition Strategy:
* Split into 3 vertical sections