Printable math worksheet for calculating perimeter and area of irregular rectangular shapes.

To solve the problem of finding the perimeter and area of each irregular rectangular shape, we need to carefully analyze each figure step by step. Below is a detailed explanation for each part:

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1. Perimeter and Area of Irregular Rectangular Shapes

#### Step 1: Understand the Problem
- Perimeter: The total length of the boundary of the shape.
- Area: The total space enclosed by the shape.

For irregular rectangular shapes, we can break them down into simpler rectangles or use the given dimensions directly.

#### Step 2: Solve Each Shape Individually

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Shape 1:

- Dimensions:
- Top side = 16
- Bottom side = 20
- Left side = 9
- Right side = 4 + 6 = 10

- Perimeter:
\[
P = 16 + 20 + 9 + 10 = 55
\]

- Area:
- Break into two rectangles:
- Rectangle 1: \(9 \times 16\)
- Rectangle 2: \(6 \times 4\)
\[
A = (9 \times 16) + (6 \times 4) = 144 + 24 = 168
\]

- Answer:
\[
P = 55, \quad A = 168
\]

---

Shape 2:

- Dimensions:
- Top side = 17
- Bottom side = 20
- Left side = 3
- Right side = 8

- Perimeter:
\[
P = 17 + 20 + 3 + 8 = 48
\]

- Area:
- Break into two rectangles:
- Rectangle 1: \(3 \times 17\)
- Rectangle 2: \(5 \times 20\)
\[
A = (3 \times 17) + (5 \times 20) = 51 + 100 = 151
\]

- Answer:
\[
P = 48, \quad A = 151
\]

---

Shape 3:

- Dimensions:
- Top side = 12
- Bottom side = 21
- Left side = 5
- Right side = 11

- Perimeter:
\[
P = 12 + 21 + 5 + 11 = 49
\]

- Area:
- Break into two rectangles:
- Rectangle 1: \(5 \times 12\)
- Rectangle 2: \(6 \times 21\)
\[
A = (5 \times 12) + (6 \times 21) = 60 + 126 = 186
\]

- Answer:
\[
P = 49, \quad A = 186
\]

---

Shape 4:

- Dimensions:
- Top side = 25
- Bottom side = 8
- Left side = 3
- Right side = 5

- Perimeter:
\[
P = 25 + 8 + 3 + 5 = 41
\]

- Area:
- Break into two rectangles:
- Rectangle 1: \(3 \times 25\)
- Rectangle 2: \(5 \times 8\)
\[
A = (3 \times 25) + (5 \times 8) = 75 + 40 = 115
\]

- Answer:
\[
P = 41, \quad A = 115
\]

---

Shape 5:

- Dimensions:
- Top side = 7
- Bottom side = 28
- Left side = 10
- Right side = 21

- Perimeter:
\[
P = 7 + 28 + 10 + 21 = 66
\]

- Area:
- Break into two rectangles:
- Rectangle 1: \(10 \times 7\)
- Rectangle 2: \(18 \times 28\)
\[
A = (10 \times 7) + (18 \times 28) = 70 + 504 = 574
\]

- Answer:
\[
P = 66, \quad A = 574
\]

---

Shape 6:

- Dimensions:
- Top side = 21
- Bottom side = 14
- Left side = 9
- Right side = 22

- Perimeter:
\[
P = 21 + 14 + 9 + 22 = 66
\]

- Area:
- Break into two rectangles:
- Rectangle 1: \(9 \times 21\)
- Rectangle 2: \(13 \times 14\)
\[
A = (9 \times 21) + (13 \times 14) = 189 + 182 = 371
\]

- Answer:
\[
P = 66, \quad A = 371
\]

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Final Answers:

1. \( P = 55, \quad A = 168 \)
2. \( P = 48, \quad A = 151 \)
3. \( P = 49, \quad A = 186 \)
4. \( P = 41, \quad A = 115 \)
5. \( P = 66, \quad A = 574 \)
6. \( P = 66, \quad A = 371 \)

\boxed{
\begin{array}{ll}
1. & P = 55, \quad A = 168 \\
2. & P = 48, \quad A = 151 \\
3. & P = 49, \quad A = 186 \\
4. & P = 41, \quad A = 115 \\
5. & P = 66, \quad A = 574 \\
6. & P = 66, \quad A = 371 \\
\end{array}
}