Geometry worksheet for calculating area and perimeter of irregular shapes.

Here are the step-by-step solutions for finding the area and perimeter of each irregular shape.

General Tips:
* Perimeter: Add up the lengths of all the outside edges. For these "L" or "step" shapes, you can often just add the two longest sides (total width and total height) and multiply by 2, because the indented sides push out to match the total length.
* Area: Split the shape into two simple rectangles. Calculate the area of each rectangle ($Length \times Width$) and add them together.

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1. Shape 1

* Dimensions: Total bottom = 25 in, Left side = 10 in, Top right part = 15 in, Inner vertical drop = 4 in.
* Missing Side Calculation:
* The top-left horizontal part is $25 - 15 = 10$ in.
* The bottom-right vertical part is $10 - 4 = 6$ in.
* Perimeter: $10 + 10 + 4 + 15 + 6 + 25 = \mathbf{70 \text{ in}}$
* Area:
* Split vertically into a left rectangle ($10 \times 10$) and a right rectangle ($15 \times 6$).
* Area = $(10 \times 10) + (15 \times 6) = 100 + 90 = \mathbf{190 \text{ sq in}}$

2. Shape 2

* Dimensions: Top = 33 in, Right = 23 in, Bottom-left indent = 12 in, Inner horizontal = 13 in.
* Missing Side Calculation:
* The left vertical side is $23 - 12 = 11$ in.
* The bottom-right horizontal part is $33 - 13 = 20$ in.
* Perimeter: $33 + 23 + 20 + 12 + 13 + 11 = \mathbf{112 \text{ in}}$
* Area:
* Split horizontally into a top rectangle ($33 \times 11$) and a bottom-right rectangle ($20 \times 12$).
* Area = $(33 \times 11) + (20 \times 12) = 363 + 240 = \mathbf{603 \text{ sq in}}$

3. Shape 3

* Dimensions: Top = 18 in, Right = 15 in, Left-top = 5 in, Bottom-left indent = 6 in.
* Missing Side Calculation:
* The bottom-right horizontal part is $18 - 6 = 12$ in.
* The inner vertical rise is $15 - 5 = 10$ in.
* Perimeter: $18 + 15 + 12 + 10 + 6 + 5 = \mathbf{66 \text{ in}}$
* Area:
* Split vertically into a left rectangle ($6 \times 5$) and a right rectangle ($12 \times 15$).
* Area = $(6 \times 5) + (12 \times 15) = 30 + 180 = \mathbf{210 \text{ sq in}}$

4. Shape 4

* Dimensions: Left = 26 ft, Bottom = 38 ft, Top-right indent = 11 ft, Inner horizontal = 19 ft.
* Missing Side Calculation:
* The top-left horizontal part is $38 - 19 = 19$ ft.
* The bottom-right vertical part is $26 - 11 = 15$ ft.
* Perimeter: $26 + 19 + 11 + 19 + 15 + 38 = \mathbf{128 \text{ ft}}$
* Area:
* Split vertically into a left rectangle ($19 \times 26$) and a right rectangle ($19 \times 15$).
* Area = $(19 \times 26) + (19 \times 15) = 494 + 285 = \mathbf{779 \text{ sq ft}}$

5. Shape 5

* Dimensions: Top = 27 yd, Right = 10 yd, Bottom-left = 16 yd, Inner vertical drop = 3 yd.
* Missing Side Calculation:
* The top-right horizontal part is $27 - 16 = 11$ yd.
* The bottom-right vertical part is $10 - 3 = 7$ yd.
* Perimeter: $27 + 10 + 11 + 3 + 16 + 7 = \mathbf{74 \text{ yd}}$
* Area:
* Split vertically into a left rectangle ($16 \times 7$) and a right rectangle ($11 \times 10$).
* Area = $(16 \times 7) + (11 \times 10) = 112 + 110 = \mathbf{222 \text{ sq yd}}$

6. Shape 6

* Dimensions: This is a regular rectangle. Length = 34 yd, Width = 9 yd.
* Perimeter: $2 \times (34 + 9) = 2 \times 43 = \mathbf{86 \text{ yd}}$
* Area: $34 \times 9 = \mathbf{306 \text{ sq yd}}$

7. Shape 7

* Dimensions: Top = 38 in, Right = 9 in, Left-top = 15 in, Inner vertical drop = 4 in.
* Missing Side Calculation:
* The bottom-right horizontal part is $38 - 15 = 23$ in.
* The bottom-left vertical part is $9 - 4 = 5$ in.
* Perimeter: $38 + 9 + 23 + 4 + 15 + 5 = \mathbf{94 \text{ in}}$
* Area:
* Split vertically into a left rectangle ($15 \times 5$) and a right rectangle ($23 \times 9$).
* Area = $(15 \times 5) + (23 \times 9) = 75 + 207 = \mathbf{282 \text{ sq in}}$

8. Shape 8

* Dimensions: Left = 26 yd, Bottom = 48 yd, Top-right indent = 11 yd, Inner horizontal = 24 yd.
* Missing Side Calculation:
* The top-left horizontal part is $48 - 24 = 24$ yd.
* The bottom-right vertical part is $26 - 11 = 15$ yd.
* Perimeter: $26 + 24 + 11 + 24 + 15 + 48 = \mathbf{148 \text{ yd}}$
* Area:
* Split vertically into a left rectangle ($24 \times 26$) and a right rectangle ($24 \times 15$).
* Area = $(24 \times 26) + (24 \times 15) = 624 + 360 = \mathbf{984 \text{ sq yd}}$

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Final Answer:

1. Area: 190 sq in, Perimeter: 70 in
2. Area: 603 sq in, Perimeter: 112 in
3. Area: 210 sq in, Perimeter: 66 in
4. Area: 779 sq ft, Perimeter: 128 ft
5. Area: 222 sq yd, Perimeter: 74 yd
6. Area: 306 sq yd, Perimeter: 86 yd
7. Area: 282 sq in, Perimeter: 94 in
8. Area: 984 sq yd, Perimeter: 148 yd