Finding Area and Perimeter of Irregular shapes - Math Worksheets ... - Free Printable

The user wants me to solve the math problems from the provided image.
The image is a worksheet titled "Geometry Worksheets: Find the Area and perimeter of irregular shapes".
There are 8 numbered problems.
I need to calculate the Area and Perimeter for each shape.

Problem 1:
- Shape: L-shaped polygon.
- Dimensions given:
- Left vertical side: 10 in
- Top horizontal segment (left part): Not explicitly given, but bottom is 25 and right part is 15. Wait, let's look closer.
- Top vertical segment (right part): 4 in.
- Middle horizontal segment: 15 in.
- Bottom horizontal segment: 25 in.
- Let's deduce missing sides.
- Total width (bottom) = 25 in.
- Top part horizontal width = Total width - Middle horizontal part? No, that's not right. Let's look at the shape again.
- It looks like a large rectangle with a chunk taken out of the top right.
- Let's assume it's composed of two rectangles.
- Rectangle 1 (Left): Height = 10 in. Width = ?
- Rectangle 2 (Right/Bottom): Height = ? Width = 15 in.
- Wait, let's look at the labels again.
- Left side: 10 in.
- Top side (left part): Unknown.
- "Step" down: 4 in.
- Horizontal part to the right: 15 in.
- Bottom side: 25 in.
- Right side: Unknown.
- Let's re-evaluate.
- If the bottom is 25 in, and the top horizontal segment is 15 in... wait, the label "15 in" is on the horizontal segment in the middle.
- So, top-left horizontal width = Total width (25) - 15 = 10 in.
- Let's check vertical sides.
- Left side = 10 in.
- The "step" down is 4 in.
- So the rightmost vertical side must be 10 - 4 = 6 in.
- Let's verify.
- Area Method 1: Split into two rectangles.
- Rectangle A (Left): Width = 10 in (calculated as 25 - 15), Height = 10 in. Area = 10 * 10 = 100 sq in.
- Rectangle B (Right): Width = 15 in, Height = 6 in (calculated as 10 - 4). Area = 15 * 6 = 90 sq in.
- Total Area = 100 + 90 = 190 sq in.
- Area Method 2: Big rectangle minus missing corner.
- Big rectangle: Width = 25, Height = 10. Area = 250.
- Missing top-right corner: Width = 15, Height = 4. Area = 60.
- Total Area = 250 - 60 = 190 sq in.
- Perimeter: Sum of all outer sides.
- Left: 10
- Top: 10 (calculated as 25 - 15)
- Down: 4
- Right-ish: 15
- Bottom: 25
- Rightmost: 6 (calculated as 10 - 4)
- Perimeter = 10 + 10 + 4 + 15 + 25 + 6 = 70 in.
- Wait, let's re-check the "Top" calculation.
- Bottom is 25. The horizontal segment labeled 15 is the upper horizontal part.
- So the top-left horizontal part is 25 - 15 = 10.
- Left side is 10.
- The vertical drop is 4.
- So the rightmost vertical side is 10 - 4 = 6.
- Perimeter = 10 (left) + 10 (top) + 4 (down) + 15 (right horizontal) + 6 (right vertical) + 25 (bottom).
- Sum: 10 + 10 + 4 + 15 + 6 + 25 = 70 in.

Problem 2:
- Shape: Inverted L-shape (or step shape).
- Dimensions:
- Top: 33 in
- Left vertical (top part): Unknown.
- Middle horizontal (left part): 13 in.
- Middle vertical (down): 12 in.
- Right vertical: 23 in.
- Let's deduce missing sides.
- Total width (top) = 33 in.
- Bottom width = 13 + (unknown right part)? No, looking at the shape, it's a rectangle with a chunk missing from the bottom left.
- Actually, it looks like a rectangle with a chunk missing from the bottom left corner? No, the "12 in" and "13 in" label an inner corner.
- Let's trace the perimeter clockwise from top left.
- Top: 33 in.
- Right side: 23 in.
- Bottom side: Unknown.
- Left vertical (lower part): 12 in.
- Middle horizontal (left part): 13 in.
- Left vertical (upper part): Unknown.
- Let's assume it's a big rectangle with a piece missing.
- Total width = 33.
- Total height = 23.
- The cutout is at the bottom left? No, looking at the lines...
- Top side: 33 in.
- Right side: 23 in.
- Bottom side: Let's call it X.
- Then going up: 12 in.
- Then left: 13 in.
- Then up: Y.
- So, Total Width (33) = Bottom part + 13. So Bottom part = 33 - 13 = 20 in. Wait, looking at the diagram, the "13 in" is the top part of the left section. The "12 in" is the vertical side dropping down.
- Let's look really closely at crop 2.
- Top side: 33 in.
- Left side has a segment labeled 13 in (horizontal) and a segment labeled 12 in (vertical).
- Right side: 23 in.
- This shape looks like a rectangle with a notch cut out of the bottom left.
- Let's assume the top side (33) corresponds to the total width.
- The right side (23) corresponds to the total height.
- The "13 in" is a horizontal segment on the left.
- The "12 in" is a vertical segment below the 13 in segment? No, looking at the corner...
- It looks like the top left corner is intact. Then it goes right 33. Then down 23. Then left... wait.
- Let's trace: Top side (33). Right side (23). Bottom side (unknown). Then up 12. Then left 13. Then up... to the top left corner.
- So, the missing vertical side on the left = Total Height (23) - 12 = 11 in.
- The missing horizontal side on the bottom = Total Width (33) - 13 = 20 in.
- Wait, let's look at the shape again.
- It looks like an L-shape rotated.
- Top horizontal: 33 in.
- Right vertical: 23 in.
- Bottom horizontal: Let's assume it aligns with the top? No.
- Let's assume the shape is composed of two rectangles.
- Rectangle 1 (Top): Width 33, Height X.
- Rectangle 2 (Bottom Right): Width Y, Height 12? No.
- Let's look at the labels "13 in" and "12 in". They are next to the inner corner.
- It looks like the shape is a large rectangle (33 wide, 23 high) with a rectangle cut out from the bottom left.
- The cutout has width 13 and height 12? No, the labels are on the *inside* edges.
- So, the horizontal segment going right from the left edge is 13. The vertical segment going down is 12.
- This implies the "missing" part is the bottom left corner.
- So, the shape has:
- Top side: 33.
- Right side: 23.
- Bottom side: 33 - 13 = 20. (Because total width is 33, top part is 13? No, 13 is the horizontal part of the "step").
- Let's re-examine.
- Top edge: 33 in.
- Left edge (top part): Unknown.
- Then a horizontal segment going right: 13 in.
- Then a vertical segment going down: 12 in.
- Then a bottom horizontal segment.
- Then a right vertical segment: 23 in.
- This interpretation doesn't fit a closed loop.
- Let's try again.
- Top edge: 33 in.
- Right edge: 23 in.
- Bottom edge: Unknown.
- Left edge (bottom part): 12 in.
- Middle horizontal edge: 13 in.
- Left edge (top part): Unknown.
- This looks like a rectangle with the bottom-left corner removed.
- Total Width = 33 in (top edge).
- Total Height = 23 in (right edge).
- The "cutout" is defined by the inner corner.
- The horizontal segment of the cutout is 13 in.
- The vertical segment of the cutout is 12 in.
- So, the bottom edge length = Total Width (33) - 13 = 20 in.
- The left edge (top part) length = Total Height (23) - 12 = 11 in.
- Area: Total Area (33 * 23) - Cutout Area (13 * 12).
- Total Area = 33 * 23 = 33 * (20 + 3) = 660 + 99 = 759.
- Cutout Area = 13 * 12 = 156.
- Shape Area = 759 - 156 = 603 sq in.
- Perimeter: Sum of outer edges.
- Top: 33
- Right: 23
- Bottom: 20 (33 - 13)
- Left (lower): 12
- Middle horizontal: 13
- Left (upper): 11 (23 - 12)
- Sum: 33 + 23 + 20 + 12 + 13 + 11 = 112 in.
- Wait, simpler perimeter rule for rectilinear shapes: Perimeter = 2 * (Total Width + Total Height).
- Perimeter = 2 * (33 + 23) = 2 * 56 = 112 in.
- Let's verify. 33 (top) + 23 (right) + 20 (bottom) + 12 (up) + 13 (left) + 11 (up).
- 33 + 23 + 20 + 12 + 13 + 11.
- 33 + 23 = 56.
- 20 + 13 = 33.
- 12 + 11 = 23.
- Total = 56 + 33 + 23 = 112. Correct.

Problem 3:
- Shape: Inverted L-shape (top heavy).
- Dimensions:
- Top: 18 in.
- Right vertical: 15 in.
- Left vertical (top part): 5 in.
- Middle horizontal: 6 in.
- Let's deduce.
- It looks like a rectangle with a chunk missing from the bottom left.
- Total Width = 18 in.
- Total Height = 15 in.
- Missing part is bottom left.
- The "5 in" is the top part of the left side.
- The "6 in" is the horizontal segment sticking out to the right from the left side? No.
- Let's look at the labels.
- "5 in" is next to the top part of the left vertical side.
- "6 in" is next to the bottom horizontal segment of the left part? No, it's under the "5 in" label. It looks like the horizontal segment of the cutout.
- "15 in" is the total right side.
- So, Left side (total) = 15 in.
- Top part of left side = 5 in.
- So the bottom part of the left side (the vertical drop of the cutout) = 15 - 5 = 10 in.
- Wait, let's look at the shape.
- It's a rectangle 18 wide and