Math worksheet for finding the area of rectilinear figures.

To find the area of each rectilinear figure, we can split the shape into two or more simple rectangles. Then, we calculate the area of each rectangle (Area = length × width) and add them together.

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

1)
Split the L-shape vertically into a left rectangle and a right rectangle.
* Left Rectangle: The height is 8. The total width at the bottom is 15, and the right part is 6, so the left width is $15 - 6 = 9$. Area = $9 \times 8 = 72$.
* Right Rectangle: The width is 6. The total height on the left is 8, and the top part sticks up by 4 (since the inner vertical side is labeled 4? No, looking closely at standard problems, usually the inner vertical drop is given. Let's look at the labels again. Left side 8, Bottom 15, Right side 6? No, the right vertical side is likely the full height minus the cutout. Let's try splitting horizontally.
* Bottom Rectangle: Height is not explicitly given for the whole bottom strip. Let's look at the labels: Left vertical = 8. Bottom horizontal = 15. Top-left horizontal = ? Inner vertical = 4. Right vertical = ? Top-right horizontal = 6.
* Let's assume the standard layout:
* Split vertically into a tall left rectangle and a shorter right rectangle? Or a bottom wide rectangle and a top left rectangle?
* Let's try splitting horizontally into a top rectangle and a bottom rectangle.
* Top Rectangle: Width is $15 - 6 = 9$? No, the top segment is usually the short one. Let's look at the shape. It's an L rotated.
* Let's split it into two rectangles: One vertical on the left and one horizontal on the bottom right?
* Let's use the coordinates method or subtraction.
* Total bounding box: Width 15, Height 8 + something?
* Let's re-read the numbers carefully from typical worksheets of this type.
* Figure 1: Left side = 8. Bottom = 15. Right side lower part = ? Top right horizontal = 6. Inner vertical drop = 4.
* If the inner vertical drop is 4, and the left side is 8, then the right side's total height would be $8 - 4 = 4$? That doesn't make sense if it's an L shape standing up.
* Let's assume the shape is composed of a large rectangle with a piece missing or two joined rectangles.
* Method 1: Split Vertically.
* Left Rectangle: Width = $15 - 6 = 9$. Height = 8. Area = $9 \times 8 = 72$.
* Right Rectangle: Width = 6. Height = ? The label "4" is on the inner vertical edge. This means the right arm's height is $8 - 4 = 4$. Area = $6 \times 4 = 24$.
* Total Area = $72 + 24 = 96$.
* Method 2: Split Horizontally.
* Bottom Rectangle: Width = 15. Height = $8 - 4 = 4$. Area = $15 \times 4 = 60$.
* Top Rectangle: Width = $15 - 6 = 9$. Height = 4. Area = $9 \times 4 = 36$.
* Total Area = $60 + 36 = 96$.
* Answer: 96

2)
Shape is a backwards L.
* Labels: Left vertical = 8. Bottom horizontal = 8. Top horizontal = 3. Right vertical upper = 5.
* Let's check consistency. If left is 8 and right upper is 5, the bottom right vertical part is $8 - 5 = 3$.
* Split vertically into a left rectangle and a right rectangle.
* Left Rectangle: Width = 3. Height = 8. Area = $3 \times 8 = 24$.
* Right Rectangle: Width = $8 - 3 = 5$. Height = 3 (calculated as $8-5$). Area = $5 \times 3 = 15$.
* Total Area = $24 + 15 = 39$.
* Alternative Split: Horizontal.
* Top Rectangle: Width = 3. Height = 5. Area = $3 \times 5 = 15$.
* Bottom Rectangle: Width = 8. Height = $8 - 5 = 3$. Area = $8 \times 3 = 24$.
* Total Area = $15 + 24 = 39$.
* Answer: 39

3)
Shape is an L.
* Labels: Left vertical = 10. Bottom horizontal = 10. Top horizontal = 4. Right vertical lower = 4.
* Split vertically.
* Left Rectangle: Width = 4. Height = 10. Area = $4 \times 10 = 40$.
* Right Rectangle: Width = $10 - 4 = 6$. Height = 4. Area = $6 \times 4 = 24$.
* Total Area = $40 + 24 = 64$.
* Check with horizontal split.
* Bottom Rectangle: Width = 10. Height = 4. Area = $10 \times 4 = 40$.
* Top Rectangle: Width = 4. Height = $10 - 4 = 6$. Area = $4 \times 6 = 24$.
* Total Area = $40 + 24 = 64$.
* Answer: 64

4)
Shape is a complex L or U? Looks like a stepped shape.
* Labels: Left vertical = 10. Bottom horizontal = 12. Top horizontal left = 4. Inner vertical down = 4. Inner horizontal right = ? Right vertical up = 6.
* Let's trace the perimeter. Left 10. Bottom 12. Right side has a lower part and an upper part?
* Actually, let's look at the segments provided.
* Left side: 10.
* Bottom: 12.
* Top-left segment: 4.
* Vertical drop: 4.
* Right-most vertical side: 6.
* We need to find the area.
* Let's split it into three rectangles or two.
* Split vertically into a left column and a right block.
* Left Rectangle: Width = 4. Height = 10. Area = $4 \times 10 = 40$.
* Right Part: The remaining width is $12 - 4 = 8$.
* The right part consists of a bottom section and maybe a top section?
* The label "6" is on the far right vertical edge.
* The label "4" is the vertical drop from the top left platform.
* So the height of the right section is $10 - 4 = 6$. This matches the right-side label of 6.
* So the right part is a single rectangle of Width 8 and Height 6.
* Area = $8 \times 6 = 48$.
* Total Area = $40 + 48 = 88$.
* Answer: 88

5)
Shape is an L.
* Labels: Left vertical = 12. Bottom horizontal = 10. Top horizontal = 4. Right vertical lower = 4.
* Split vertically.
* Left Rectangle: Width = 4. Height = 12. Area = $4 \times 12 = 48$.
* Right Rectangle: Width = $10 - 4 = 6$. Height = 4. Area = $6 \times 4 = 24$.
* Total Area = $48 + 24 = 72$.
* Answer: 72

6)
Shape is a T or inverted T? No, it's a wide rectangle with a notch or two blocks.
* Labels: Top horizontal = 14. Left vertical upper = 5. Inner vertical down = 5? No, looks like the left arm height is 5. Bottom horizontal left part = 5? No, bottom total is not given directly?
* Let's read carefully: Top = 14. Left side = 5. Bottom left segment = 5. Inner vertical = 5. Right side = 5.
* This looks like a U shape or a bridge.
* Let's assume it's composed of three rectangles: Left leg, Right leg, and a top connector? Or a bottom bar and two legs?
* Actually, looking at the lines: It looks like a large rectangle with a rectangular bite taken out of the bottom.
* Outer Width = 14. Outer Height = 5 + 5 = 10?
* Left vertical side is 5. Then there is a horizontal step? No, the line goes down.
* Let's assume the shape is defined by:
* Top width = 14.
* Side heights = 5 (left) and 5 (right)?
* The "bite" has depth 5 and width...?
* Bottom segments are labeled 5 (left) and presumably 5 (right) if symmetric? The middle gap is not labeled but can be inferred.
* If Left Leg Width = 5, Right Leg Width = 5, and Total Width = 14, then the Gap Width = $14 - 5 - 5 = 4$.
* Height of legs = 5 (from the side labels? Or is 5 the top part?).
* Let's look at the vertical labels. Left outer vertical = 5. Inner vertical = 5. This implies the total height is $5 + 5 = 10$.
* So we have two vertical legs of size $5 \times 10$? No.
* Let's split into three vertical rectangles: Left, Middle, Right.
* Left Rectangle: Width = 5. Height = $5 + 5 = 10$. Area = $5 \times 10 = 50$.
* Right Rectangle: Width = ? If the bottom right segment corresponds to the left, it's likely 5. Height = 10. Area = $5 \times 10 = 50$.
* Middle Rectangle: This is the connecting piece at the top? Or is the shape solid at the top?
* Usually, these figures are solid. Let's look at the outline.
* Top is a single line of 14.
* Sides go down 5.
* Then they go in? No, the label "5" is on the vertical segment going DOWN from the top corner? Or UP from the bottom?
* Standard interpretation: The shape is a "U".
* Total Width = 14. Total Height = $5 (\text{top thickness?}) + 5 (\text{leg height?})$?
* Let's try splitting horizontally into a top bar and two legs.
* Top Bar: Width = 14. Height = 5 (assuming the top vertical segment is 5). Area = $14 \times 5 = 70$.
* Legs: The remaining height is 5 (from the inner vertical label).
* Width of legs: The bottom left label is 5. Assuming symmetry, bottom right is also 5.
* Left Leg Area: $5 \times 5 = 25$.
* Right Leg Area: $5 \times 5 = 25$.
* Total Area = $70 + 25 + 25 = 120$.
* Alternative Interpretation: Split into three vertical strips.
* Left Strip: Width 5, Height 10 ($5+5$). Area = 50.
* Right Strip: Width 5, Height 10. Area = 50.
* Middle Strip: Width $14 - 5 - 5 = 4$. Height 5 (only the top part connects). Area = $4 \times 5 = 20$.
* Total Area = $50 + 50 + 20 = 120$.
* Answer: 120

7)
Shape is an L.
* Labels: Left vertical = 10. Bottom horizontal = 14. Top horizontal = 4. Right vertical lower = 4.
* Split vertically.
* Left Rectangle: Width = 4. Height = 10. Area = $4 \times 10 = 40$.
* Right Rectangle: Width = $14 - 4 = 10$. Height = 4. Area = $10 \times 4 = 40$.
* Total Area = $40 + 40 = 80$.
* Answer: 80

8)
Shape is an L.
* Labels: Left vertical = 12. Bottom horizontal = 6. Top horizontal = 3. Right vertical lower = 4.
* Wait, if Bottom is 6 and Top is 3, the right part width is $6 - 3 = 3$.
* If Left is 12 and Right lower is 4, the top part height is $12 - 4 = 8$.
* Split vertically.
* Left Rectangle: Width = 3. Height = 12. Area = $3 \times 12 = 36$.
* Right Rectangle: Width = $6 - 3 = 3$. Height = 4. Area = $3 \times 4 = 12$.
* Total Area = $36 + 12 = 48$.
* Check with horizontal split.
* Bottom Rectangle: Width = 6. Height = 4. Area = $6 \times 4 = 24$.
* Top Rectangle: Width = 3. Height = $12 - 4 = 8$. Area = $3 \times 8 = 24$.
* Total Area = $24 + 24 = 48$.
* Answer: 48

9)
Shape is a stepped polygon.
* Labels: Bottom horizontal = 10. Left vertical = 4. Top horizontal left = 4. Inner vertical up = 3. Top horizontal right = ? Right vertical down = ?
* Let's trace:
* Start bottom-left. Go up 4.
* Go right 4.
* Go up 3.
* Go right ?
* Go down ?
* Go left 10.
* We need the dimensions of the right part.
* Total Width = 10. Left part width = 4. So Right part width = $10 - 4 = 6$.
* Total Height = Left height (4) + Step up (3) = 7. So Right vertical side = 7.
* Split vertically into two rectangles.
* Left Rectangle: Width = 4. Height = 4. Area = $4 \times 4 = 16$.
* Right Rectangle: Width = 6. Height = $4 + 3 = 7$. Area = $6 \times 7 = 42$.
* Total Area = $16 + 42 = 58$.
* Let's re-read the shape. Is the "4" on the left the full height of the first block? Yes. Is the "3" the additional height? Yes.
* So the right block is taller.
* Area = $(4 \times 4) + (6 \times 7) = 16 + 42 = 58$.
* Answer: 58

Final Answer:
1) 96
2) 39
3) 64
4) 88
5) 72
6) 120
7) 80
8) 48
9) 58