Area of Compound Shapes - Free Printable

To find the area of compound shapes, we break them down into simpler shapes like rectangles and triangles. Then we calculate the area of each part and add them together.

Here is the step-by-step solution for each shape:

1. Top Left Shape
* Breakdown: A rectangle on top and a triangle on the bottom right? No, looking at the dashed line, it splits into a tall rectangle on the left and a triangle on the right.
* Actually, let's look closer. The dashed line goes down from the inner corner. This creates a rectangle on the left and a triangle on the right.
* Rectangle: Width = 4 cm, Height = 9 cm. Area = $4 \times 9 = 36 \text{ cm}^2$.
* Triangle: The base is given as 5 cm. The height corresponds to the vertical drop from the top of the rectangle section. The total height on the left is 9 cm. The vertical segment labeled "3 cm" is the part of the side *above* the triangle's start? Or is it the height of the triangle? Let's re-examine.
* Alternative breakdown: A large rectangle minus a missing piece? Or a rectangle plus a triangle.
* Let's look at the labels again. Left side is 9 cm. Top width is 4 cm. There is a vertical drop of 3 cm labeled on the inner vertical edge. Then a diagonal line goes to the bottom right. The bottom horizontal segment of the triangle part is 5 cm.
* Let's split it horizontally or vertically. The dashed line is vertical. So we have a rectangle on the left and a triangle on the right.
* Left Rectangle: Width = 4 cm. Height = 9 cm. Area = $4 \times 9 = 36 \text{ cm}^2$.
* Right Triangle: Base = 5 cm. What is the height? The total height of the shape on the left is 9 cm. The label "3 cm" is on the vertical edge connecting the top rectangle part to the slanted line. Wait, the diagram shows the top part is a rectangle of $4 \times ?$ and the bottom is... no.
* Let's look at the standard interpretation: The shape is composed of a rectangle and a triangle. The dashed line separates them.
* Left part: Rectangle with width 4 cm and height 9 cm. Area = $36 \text{ cm}^2$.
* Right part: Triangle with base 5 cm. Its height is determined by the vertical side it shares with the rectangle? No, the triangle is attached to the side.
* Let's try splitting it horizontally.
* Top Rectangle: Width 4 cm. Height? The label "3 cm" is next to the vertical segment below the top edge? No, it's inside.
* Let's assume the dashed line indicates the separation.
* Shape 1 (Left): Rectangle. Width = 4 cm. Height = 9 cm. Area = $36 \text{ cm}^2$.
* Shape 2 (Right): Triangle. Base = 5 cm. Height = ? The triangle starts at the bottom of the "3 cm" segment? No.
* Let's look at the vertices. Top-left (0,9), Top-right-inner (4,9), Inner-corner (4,6) because the drop is 3cm? If the drop is 3cm from the top, then the y-coordinate is $9-3=6$. Then the line goes to (4+5, 0) = (9,0)? And the bottom left is (0,0).
* If this is the case:
* Rectangle part: Width 4, Height 6? No, the left side is 9.
* Let's assume the shape is a large rectangle ($4 \times 9$) plus a triangle? No.
* Let's assume the shape is a trapezoid + rectangle?
* Let's try this common pattern: The shape is a rectangle ($4 \times 9$) and a triangle attached to the side? No, the outline is continuous.
* Let's look at the dashed line again. It drops from the inner corner to the bottom. This implies the shape is split into a left rectangle and a right triangle.
* Left Rectangle: Width = 4 cm. Height = 9 cm. Area = $36 \text{ cm}^2$.
* Right Triangle: Base = 5 cm. Height = The vertical distance from the inner corner to the bottom. The inner corner is at the top of the triangle. The label "3 cm" is on the vertical segment *above* the triangle? No, the label "3 cm" is on the vertical edge of the "cutout" or the step.
* Actually, usually these diagrams label the segments of the perimeter.
* Left vertical: 9 cm.
* Top horizontal: 4 cm.
* Inner vertical down: 3 cm.
* Bottom horizontal right part: 5 cm.
* This implies the height of the triangle is the remaining height of the left side? No.
* If the left side is 9, and the inner vertical drop is 3, does that mean the triangle's height is $9 - 3 = 6$? Or is the triangle's height just the vertical span of the slanted line?
* Let's assume the bottom line is flat. Then the height of the triangle is the difference between the total height (9) and the top segment height? No.
* Let's look at the coordinates.
* Start at bottom-left (0,0). Go up to (0,9). Go right to (4,9). Go down to (4, 6) [since the segment is 3cm long]. Then go diagonally to (9, 0) [since base is 5cm wider than 4? No, the 5cm is the base of the triangle].
* If the triangle base is 5, and it sits on the same baseline as the rectangle, then the vertex is at (4+5, 0) = (9,0).
* The triangle connects (4,6) to (9,0) and (4,0).
* So the triangle has Base = 5 cm and Height = 6 cm (from y=0 to y=6).
* Area of Triangle = $0.5 \times 5 \times 6 = 15 \text{ cm}^2$.
* Area of Rectangle (left part) = Width 4 $\times$ Height 9? No. The rectangle part in this decomposition would be from x=0 to 4, y=0 to 9. But the shape boundary goes from (4,9) down to (4,6). So the region x=0..4, y=0..9 is fully included? Yes.
* So, Area = Area of Rectangle ($4 \times 9$) + Area of Triangle?
* Wait, if the rectangle is $4 \times 9$, its right edge is at x=4, from y=0 to y=9. The triangle is attached to the segment from (4,0) to (4,6)? No, the shape boundary goes (4,9) -> (4,6) -> (9,0).
* This means the shape consists of:
1. A rectangle of width 4 and height 9? No, because the right side of the rectangle would be the line x=4. The shape includes the area to the left of x=4. So yes, Rectangle Area = $4 \times 9 = 36$.
2. Plus a triangle? The triangle is defined by points (4,6), (4,0), and (9,0). This triangle is to the right of the rectangle.
3. Is the space between y=6 and y=9 at x>4 empty? Yes.
4. So Total Area = Area(Rectangle $4 \times 9$) + Area(Triangle with base 5, height 6).
5. Triangle Height: The vertical side of the triangle is along the line x=4. It goes from y=0 to y=6. So height is 6.
6. Triangle Area = $\frac{1}{2} \times 5 \times 6 = 15$.
7. Total Area = $36 + 15 = 51 \text{ cm}^2$.

* *Alternative Interpretation:* Maybe the "3 cm" is the height of the top rectangular part above the triangle?
* If the shape is split horizontally:
* Top Rectangle: $4 \times 3 = 12$.
* Bottom Trapezoid? No.
* Bottom Rectangle: $4 \times (9-3) = 24$.
* Triangle attached to side: Base 5, Height $(9-3)=6$. Area = 15.
* Total = $12 + 24 + 15 = 51$. Same result.

* Answer 1: 51 cm²

2. Top Middle Shape
* Breakdown: A rectangle and a triangle.
* Rectangle: Width = 3 cm, Height = 6 cm. Area = $3 \times 6 = 18 \text{ cm}^2$.
* Triangle: Base = 3 cm. Height = Same as the rectangle's height = 6 cm. Area = $\frac{1}{2} \times 3 \times 6 = 9 \text{ cm}^2$.
* Total Area: $18 + 9 = 27 \text{ cm}^2$.
* Answer 2: 27 cm²

3. Top Right Shape
* Breakdown: A rectangle and a trapezoid? Or a rectangle and two triangles?
* The dashed line is horizontal. It splits the shape into a bottom rectangle and a top trapezoid? No, the top part is a triangle on top of a rectangle?
* Let's look at the dimensions.
* Bottom part: Height = 6 cm. Width = 8 cm. This looks like a rectangle. Area = $8 \times 6 = 48 \text{ cm}^2$.
* Top part: It sits on top of the 8 cm width. But the shape slopes.
* Left vertical side total height isn't given directly, but the bottom part is 6, top part has a vertical label "3 cm". So the top section height is 3 cm.
* The top section is a trapezoid? Or a triangle + rectangle?
* The dashed line is at height 6. Above it, on the left, there is a vertical segment of 3 cm. So the top-left corner is at height $6+3=9$.
* The top boundary is a single slanted line from the top-left (height 9) to some point on the right.
* On the right side, there is a small horizontal segment labeled "1 cm" at the bottom? No, "1 cm" is the extension of the base beyond the vertical dashed line?
* Let's trace the perimeter.
* Bottom: Length 8 cm (left part) + 1 cm (right part)? The label "8 cm" is under the main block. The label "1 cm" is under the little tail.
* So total bottom width = $8 + 1 = 9$ cm?
* Right side: There is a vertical dashed line dropping from the end of the slanted roof. This suggests the shape is a large trapezoid or composite.
* Let's decompose based on the dashed lines shown.
* There is a horizontal dashed line at height 6.
* There is a vertical dashed line on the right.
* This divides the shape into:
1. Bottom-Left Rectangle: Width 8, Height 6. Area = $48 \text{ cm}^2$.
2. Top-Left Shape: It's a trapezoid? No, the left side goes up 3 cm. The top is slanted. The right boundary of this top part is the vertical dashed line. Where does the slanted line end? It seems to meet the vertical dashed line.
3. Bottom-Right Triangle? The label "1 cm" is at the bottom right. The vertical dashed line separates the 8cm part from the 1cm part.
4. So, we have a main body of width 8 and a tail of width 1.
5. Let's look at the top part above the dashed line (height 6).
* Left height is 3 cm.
* It forms a triangle? If the slanted line goes from top-left (height 9 relative to bottom, or 3 relative to dashed line) to the corner of the vertical dashed line (height 6 relative to bottom, or 0 relative to dashed line)?
* If the slanted line goes down to the level of the dashed line, then the top part is a triangle with base 8 and height 3.
* Area of Top Triangle = $\frac{1}{2} \times 8 \times 3 = 12 \text{ cm}^2$.
6. Now, what is the shape on the right (the 1 cm part)?
* It is bounded by the vertical dashed line on the left, the bottom on the bottom, and a slanted line on the right?
* Looking at the diagram, the slanted line from the top continues? No, there is a "kink". The line from the top-left goes to the top of the vertical dashed line. Then another line goes from there to the bottom-right tip?
* Actually, it looks like one continuous slanted line from top-left to bottom-right?
* If it's one straight line:
* Total width = $8 + 1 = 9$ cm? Or is the 1 cm separate?
* Let's assume the standard decomposition:
* Rectangle: $8 \times 6 = 48$.
* Triangle on top: Base 8, Height 3. Area = 12.
* Triangle on right: Base 1, Height... ? The vertex is at the top of the vertical dashed line (height 6). The bottom is at height 0. So it's a triangle with base 1 and height 6?
* Area = $\frac{1}{2} \times 1 \times 6 = 3$.
* Total Area = $48 + 12 + 3 = 63 \text{ cm}^2$.
* Let's double check this interpretation.
* Left part: Rectangle $8 \times 6$ + Triangle on top ($8 \times 3 / 2$). This forms a trapezoid with parallel vertical sides? No, parallel horizontal bases? No. It's a right trapezoid on its side?
* Vertices: (0,0), (8,0), (8,6), (0,9), (0,0). Area = Average width $\times$ height? No. Area = Rectangle + Triangle = $48 + 12 = 60$.
* Right part: Attached to the side x=8. Vertices: (8,0), (9,0), (8,6). This is a right-angled triangle. Base 1, Height 6. Area = 3.
* Total Area = $60 + 3 = 63 \text{ cm}^2$.

* Answer 3: 63 cm²

4. Middle Left Shape
* Breakdown: A square/rectangle on top and a triangle on the bottom.
* Top Rectangle: Width = 4 cm, Height = 4 cm. Area = $4 \times 4 = 16 \text{ cm}^2$.
* Bottom Triangle: Base = 4 cm (same as width of rectangle). Height = 4 cm (labeled on the right vertical extension).
* Wait, is the height 4? The label "4 cm" is on the vertical segment from the dashed line down to the bottom vertex. Yes.
* Area = $\frac{1}{2} \times 4 \times 4 = 8 \text{ cm}^2$.
* Total Area: $16 + 8 = 24 \text{ cm}^2$.
* Answer 4: 24 cm²

5. Middle Center Shape
* Breakdown: A central rectangle and two triangles (top and bottom).
* Central Rectangle: Height = 4 cm (labeled on right). Width = 10 cm (labeled on dashed line). Area = $10 \times 4 = 40 \text{ cm}^2$.
* Top Triangle: Base = 10 cm. Height = 4 cm (labeled on left vertical extension). Area = $\frac{1}{2} \times 10 \times 4 = 20 \text{ cm}^2$.
* Bottom Triangle: Base = 10 cm. Height = 3 cm (labeled on right vertical extension). Area = $\frac{1}{2} \times 10 \times 3 = 15 \text{ cm}^2$.
* Total Area: $40 + 20 + 15 = 75 \text{ cm}^2$.
* Answer 5: 75 cm²

6. Middle Right Shape
* Breakdown: A top rectangle and a bottom shape which is a rectangle minus a triangle? Or a trapezoid?
* Let's decompose using the dashed line.
* Top Rectangle: Width = 10 cm. Height = 4 cm. Area = $10 \times 4 = 40 \text{ cm}^2$.
* Bottom Part:
* Total height on left is $4 + 6 = 10$? No, the "6 cm" label is for the bottom section's height.
* So bottom section height = 6 cm.
* The bottom section is not a full rectangle. There is a cut-out triangle on the right? Or an added triangle on the left?
* Looking at the shape: The left side is vertical. The bottom is horizontal. The right side of the bottom part is slanted.
* The dashed line is at the boundary between top and bottom.
* Top width is 10.
* Bottom part: Left side is aligned with top. Right side has a horizontal segment labeled "3 cm" going inward from the right edge of the top rectangle?
* Let's trace: From the right end of the dashed line (width 10), go left 3 cm? No, the label "3 cm" is on a horizontal segment.
* It looks like the bottom shape is a trapezoid.
* Parallel sides are vertical? No.
* Let's assume the bottom shape is a rectangle of width $(10 - 3)$?
* Let's look at the vertices of the bottom part.
* Top-Left: (0, 4) relative to bottom-left origin? Let's set bottom-left at (0,0).
* Top-Left of bottom part: (0, 6).
* Top-Right of bottom part: The dashed line ends at x=10. But the shape boundary goes from (0,6) to ...?
* The label "3 cm" is on a horizontal shelf. This implies the shape indents.
* So, from the right edge of the top rectangle (x=10), the boundary goes down? No.
* Let's look at the "3 cm" label again. It is on a horizontal line segment *inside* the bottom area? No, it's on the boundary.
* It seems the bottom part is a rectangle of width 7 and a triangle?
* Let's try this: The bottom part is a large rectangle ($10 \times 6$) with a triangle removed from the bottom right?
* If a triangle is removed, the hypotenuse would be the boundary.
* The horizontal leg of the removed triangle would be 3 cm (since $10 - 7 = 3$?).
* The vertical leg would be 6 cm.
* So the remaining shape is a trapezoid with heights 6 (left) and 0 (right)? No.
* Let's look at the diagonal. It goes from bottom-left (0,0) to a point on the dashed line?
* No, the diagonal starts at the bottom-left corner and goes up to the right.
* It meets a horizontal segment of length 3 cm.
* So the vertex is at x = $10 - 3 = 7$? And y = 6?
* So the bottom part is a triangle with base 7? No.
* Let's decompose the bottom part into a rectangle and a triangle.
* Draw a vertical line up from the start of the "3 cm" segment.
* This creates a rectangle on the left and a triangle? No.
* Let's assume the bottom part is a Trapezoid.
* Parallel vertical sides? No.
* Parallel horizontal sides? The top side (dashed) is 10 cm. The bottom side is... a point? No.
* Let's look at the shape again. It's a "boot" shape.
* Top rectangle: $10 \times 4 = 40$.
* Bottom part: Left vertical side is 6 cm. Bottom horizontal side is... unknown?
* Right side: A horizontal segment of 3 cm connects to the slanted line.
* This implies the slanted line connects the bottom-left corner to the point (7, 6)?
* If so, the bottom part is a triangle with Base = 7? No, the region is under the dashed line.
* The region is bounded by: Left (x=0, y=0 to 6), Top (y=6, x=0 to 10), Right (x=10, y=6 down to...?), Bottom/Slant.
* Actually, the label "3 cm" is on the horizontal segment extending from the right wall of the top rectangle?
* No, the top rectangle is 10 wide. The bottom part is narrower on the right?
* Let's assume the bottom part is a rectangle of width 7 and height 6, PLUS a triangle?
* Or is it a rectangle of width 10 and height 6 MINUS a triangle?
* If we take the bounding box of the bottom part ($10 \times 6$), and remove the empty space on the bottom right.
* The empty space is a triangle. Its top vertex is at (10,6). Its bottom vertex is at (10,0)? No.
* The boundary goes from (0,0) to (7,6). Then horizontal to (10,6).
* So the filled area is a trapezoid with parallel vertical sides? No.
* It is a trapezoid with parallel horizontal sides?
* Top side (at y=6): Length 10.
* Bottom side (at y=0): Length 0? (It's a point at 0,0).
* This doesn't fit the "3 cm" label.
* Let's re-read the diagram.
* Top Rectangle: $10 \times 4$.
* Bottom Section:
* Left height: 6.
* There is a slanted line from bottom-left to somewhere.
* There is a horizontal segment of 3 cm on the right.
* This usually means the shape is a rectangle ($7 \times 6$) plus a triangle?
* Or a rectangle ($10 \times 6$) minus a triangle of base 3 and height 6?
* If we subtract a triangle of base 3 (horizontal) and height 6 (vertical) from the right side of a $10 \times 6$ rectangle:
* The hypotenuse would connect (7,0) to (10,6).
* But the diagram shows the slanted line starting from the bottom-left?
* Let's look really closely at the 6th image (Middle Right).
* The slanted line starts at the bottom-left corner.
* It goes up and to the right.
* It meets a horizontal line segment labeled "3 cm".
* This horizontal segment connects to the right vertical edge of the top rectangle.
* So, the vertex where the slant meets the horizontal is at x = $10 - 3 = 7$.
* The y-coordinate of this vertex is the height of the bottom section, which is 6.
* So the slanted line connects (0,0) to (7,6).
* The area under this line (bounded by x=0, y=0, y=6, and the line) is NOT the shape. The shape is to the *right* of the slant? No, the shape is the polygon.
* The polygon vertices for the bottom part are: (0,0), (0,6), (10,6), (7,6)... wait.
* If the horizontal segment is 3 cm long and ends at the right edge (x=10), it starts at x=7.
* So the boundary goes from (7,6) to (10,6).
* And the slanted line goes from (0,0) to (7,6).
* And the left boundary is (0,0) to (0,6).
* And the bottom boundary? There is no bottom boundary other than the point (0,0)?
* This would make the bottom part a triangle with vertices (0,0), (0,6), (7,6).
* Area of this triangle = $\frac{1}{2} \times \text{Base} \times \text{Height}$.
* Base (vertical) = 6. Height (horizontal) = 7. Area = $\frac{1}{2} \times 6 \times 7 = 21$.
* Plus the "empty" space? No, the shape is the union of the top rectangle and this bottom polygon.
* Wait, is the region (0,0)-(7,0)-(7,6) included?
* The diagram shows the slanted line as the *bottom-right* boundary of the left part?
* No, the shape is solid. The slanted line is a boundary.
* If the vertices are (0,0), (0,6), (10,6), (10,4)... no.
* Let's assume the standard "L-shape with a slope".
* Bottom part Area = Area of Rectangle ($7 \times 6$) + Area of Triangle?
* Let's try calculating the area of the polygon defined by (0,0), (0,6), (10,6), (7,6) is just a line.
* The polygon is (0,0) -> (0,6) -> (10,6) -> (7,6) -> (0,0)? That's a triangle (0,0)-(0,6)-(7,6) plus a rectangle (7,0)-(10,0)-(10,6)-(7,6)?
* No, the segment (7,6) to (10,6) is the top of the right part.
* Is there material below y=6 for x > 7?
* The label "3 cm" is on the segment. The segment is part of the perimeter.
* If the perimeter goes (0,0) -> (0,6) -> (10,6) -> (10,4) [up to top rect]...
* Then the bottom part is just the triangle (0,0)-(0,6)-(7,6) AND the rectangle (7,0)-(10,0)-(10,6)-(7,6)?
* If the shape included the rectangle on the right, the bottom boundary would be (0,0) to (10,0). But there is no line drawn there. The line drawn is the slant.
* This implies the area to the right of the slant and below y=6 is EMPTY?
* If so, Area = Area(Top Rect) + Area(Triangle).
* Triangle: Vertices (0,0), (0,6), (7,6). Base=6, Height=7. Area = 21.
* Top Rect: $10 \times 4 = 40$.
* Total = 61.
* BUT, look at the right side of the bottom part. Is it empty?
* Usually, these shapes are convex-ish or simple unions.
* Let's look at the alternative: The bottom part is a trapezoid.
* Parallel sides: Left vertical (6) and Right vertical (?).
* If the right side was vertical, the "3 cm" label wouldn't be horizontal.
* Let's assume the bottom part is a Trapezoid with parallel horizontal sides?
* Top side = 10.
* Bottom side = ?
* Height = 6.
* Slanted side connects bottom-left to ...?
* This doesn't fit the "3 cm" label placement.

* Let's try one more common interpretation:
* The bottom shape is a Rectangle ($10 \times 6$) with a Triangle cut out from the bottom left?
* No, the slant is on the left? No, slant starts at bottom left.
* What if the "3 cm" refers to the horizontal leg of the triangle formed by the slant?
* If the slant goes from (0,0) to (7,6), the horizontal span is 7.
* If the total width is 10, then the remaining width is 3.
* This matches the label "3 cm" being the segment from x=7 to x=10.
* So, is the area under the segment (7,6)-(10,6) filled?
* If the shape boundary is (0,0)->(0,6)->(10,6)->(10,4)... then the region x=7..10, y=0..6 is INSIDE the shape?
* If it is inside, why is the boundary (0,0) to (7,6)?
* This would mean the boundary cuts through the interior? No.
* The boundary defines the edge.
* If the edge is (0,0) to (7,6), then the material is to the top-left of this line?
* If so, the region x=7..10, y=0..6 is NOT included, because it's to the right/bottom of the slant?
* Wait, the slant has positive slope. The region "above" the slant is included.
* The region x=7..10, y=0..6 is below the line y=6.
* Is it above the slant? The slant ends at (7,6). For x>7, the slant doesn't exist.
* The boundary continues horizontally from (7,6) to (10,6).
* Then vertically up to (10,10).
* Then left to (0,10).
* Then down to (0,0).
* This encloses the Top Rectangle ($10 \times 4$) AND the region bounded by (0,0)-(0,6)-(7,6)-(10,6)-(10,4)... wait.
* If the boundary goes (7,6) to (10,6), then the corner (10,6) is a vertex.
* Then it goes up to (10,10).
* So the region x=7..10, y=0..6 is BOUNDED by:
* Top: y=6 (segment 7-10).
* Right: x=10 (segment 6-10? No, 6-4 is outside, 4-10 is top rect).
* Left: The slant? No, the slant is at x<7.
* Bottom: ??? There is no bottom boundary drawn for x=7..10.
* This implies the shape DOES NOT include the region x=7..10, y=0..6.
* Therefore, the bottom part is ONLY the triangle/trapezoid on the left.
* Specifically, the polygon (0,0)-(0,6)-(7,6).
* And the segment (7,6)-(10,6) is just the lid of the empty space?
* Yes.
* So Bottom Area = Area of Triangle with base 6 (vertical) and height 7 (horizontal).
* Area = $\frac{1}{2} \times 6 \times 7 = 21 \text{ cm}^2$.
* Top Area = $10 \times 4 = 40 \text{ cm}^2$.
* Total Area = $40 + 21 = 61 \text{ cm}^2$.

* *Self-Correction*: Does the shape look like it has a "bite" taken out? Yes.
* Answer 6: 61 cm²

7. Bottom Left Shape
* Breakdown: A rectangle and a triangle on top.
* Rectangle: Width = 12 cm, Height = 4 cm. Area = $12 \times 4 = 48 \text{ cm}^2$.
* Triangle: Sits on top of the rectangle.
* Base = 12 cm.
* Height = 4 cm (labeled on the right vertical extension).
* Area = $\frac{1}{2} \times 12 \times 4 = 24 \text{ cm}^2$.
* Total Area: $48 + 24 = 72 \text{ cm}^2$.
* Answer 7: 72 cm²

8. Bottom Middle Shape
* Breakdown: A rectangle and a trapezoid? Or two trapezoids?
* Dashed line is horizontal.
* Bottom Rectangle: Width = 18 cm. Height = 8 cm. Area = $18 \times 8 = 144 \text{ cm}^2$.
* Top Trapezoid:
* Sits on top of the rectangle.
* Bottom Base = 18 cm.
* Left Height = 6 cm (labeled on the left vertical extension).
* Right Height = 0? The slanted line goes down to the corner?
* Let's check the right side. The label "8 cm" is for the bottom part. The top part slants down to the right corner of the rectangle?
* If so, the top part is a triangle.
* Base = 18 cm. Height = 6 cm.
* Area = $\frac{1}{2} \times 18 \times 6 = 54 \text{ cm}^2$.
* Total Area = $144 + 54 = 198 \text{ cm}^2$.
* Let's verify the shape. Left side total height = $8 + 6 = 14$. Right side height = 8. Top is slanted.
* Yes, this is a trapezoid with parallel vertical sides? No, parallel horizontal bases? No.
* It's a rectangle ($18 \times 8$) plus a triangle ($18 \times 6 / 2$).
* Answer 8: 198 cm²

9. Bottom Right Shape
* Breakdown: A rectangle and a triangle.
* Rectangle: Width = 6 cm. Height = 8 cm. Area = $6 \times 8 = 48 \text{ cm}^2$.
* Triangle: Attached to the right side.
* Base (vertical) = 8 cm (shared with rectangle).
* Height (horizontal) = 5 cm (labeled on top extension? No, labeled on the top horizontal segment of the triangle? Or the projection?)
* The label "5 cm" is on the top horizontal leg of the triangle?
* The triangle is a right-angled triangle.
* Vertical leg = 8 cm.
* Horizontal leg = 5 cm.
* Area = $\frac{1}{2} \times 5 \times 8 = 20 \text{ cm}^2$.
* Total Area: $48 + 20 = 68 \text{ cm}^2$.
* Answer 9: 68 cm²

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Final Answer:
1. 51 cm²
2. 27 cm²
3. 63 cm²
4. 24 cm²
5. 75 cm²
6. 61 cm²
7. 72 cm²
8. 198 cm²
9. 68 cm²