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

To solve the problem of finding the area and perimeter of irregular shapes, we need to break each shape into simpler geometric figures (like rectangles) and then calculate the area and perimeter step by step. Let's go through each shape one by one.

---

Shape 1:

#### Dimensions:
- Top rectangle: \(10 \, \text{in} \times 4 \, \text{in}\)
- Bottom rectangle: \(25 \, \text{in} \times 15 \, \text{in}\)

#### Area:
The total area is the sum of the areas of the two rectangles.
\[
\text{Area of top rectangle} = 10 \times 4 = 40 \, \text{in}^2
\]
\[
\text{Area of bottom rectangle} = 25 \times 15 = 375 \, \text{in}^2
\]
\[
\text{Total Area} = 40 + 375 = 415 \, \text{in}^2
\]

#### Perimeter:
The perimeter is the sum of all the outer edges. The shape can be visualized as a single large rectangle with some internal lines that do not affect the perimeter.
\[
\text{Perimeter} = 2 \times (\text{length} + \text{width}) = 2 \times (25 + 19) = 2 \times 44 = 88 \, \text{in}
\]
(Note: The width is \(10 + 9 = 19 \, \text{in}\).)

---

Shape 2:

#### Dimensions:
- Top rectangle: \(33 \, \text{in} \times 13 \, \text{in}\)
- Bottom rectangle: \(23 \, \text{in} \times 12 \, \text{in}\)

#### Area:
The total area is the sum of the areas of the two rectangles.
\[
\text{Area of top rectangle} = 33 \times 13 = 429 \, \text{in}^2
\]
\[
\text{Area of bottom rectangle} = 23 \times 12 = 276 \, \text{in}^2
\]
\[
\text{Total Area} = 429 + 276 = 705 \, \text{in}^2
\]

#### Perimeter:
The perimeter is the sum of all the outer edges.
\[
\text{Perimeter} = 33 + 13 + 23 + 12 + 20 + 20 = 121 \, \text{in}
\]
(Note: The horizontal gap between the two rectangles is \(33 - 23 = 10 \, \text{in}\), so the total horizontal length is \(13 + 10 + 12 = 35 \, \text{in}\). The vertical sides are \(33\) and \(23\), and the remaining sides are \(13\) and \(12\).)

---

Shape 3:

#### Dimensions:
- Left rectangle: \(18 \, \text{in} \times 5 \, \text{in}\)
- Right rectangle: \(15 \, \text{in} \times 6 \, \text{in}\)

#### Area:
The total area is the sum of the areas of the two rectangles.
\[
\text{Area of left rectangle} = 18 \times 5 = 90 \, \text{in}^2
\]
\[
\text{Area of right rectangle} = 15 \times 6 = 90 \, \text{in}^2
\]
\[
\text{Total Area} = 90 + 90 = 180 \, \text{in}^2
\]

#### Perimeter:
The perimeter is the sum of all the outer edges.
\[
\text{Perimeter} = 18 + 5 + 15 + 6 + 13 + 13 = 70 \, \text{in}
\]
(Note: The horizontal gap between the two rectangles is \(18 - 15 = 3 \, \text{in}\), so the total horizontal length is \(5 + 3 + 6 = 14 \, \text{in}\). The vertical sides are \(18\) and \(15\), and the remaining sides are \(5\) and \(6\).)

---

Shape 4:

#### Dimensions:
- Main rectangle: \(26 \, \text{ft} \times 38 \, \text{ft}\)
- Small rectangle: \(11 \, \text{ft} \times 19 \, \text{ft}\)

#### Area:
The total area is the area of the main rectangle minus the area of the small rectangle.
\[
\text{Area of main rectangle} = 26 \times 38 = 988 \, \text{ft}^2
\]
\[
\text{Area of small rectangle} = 11 \times 19 = 209 \, \text{ft}^2
\]
\[
\text{Total Area} = 988 - 209 = 779 \, \text{ft}^2
\]

#### Perimeter:
The perimeter is the sum of all the outer edges.
\[
\text{Perimeter} = 26 + 38 + 26 + 38 = 128 \, \text{ft}
\]
(Note: The small rectangle does not affect the outer perimeter.)

---

Shape 5:

#### Dimensions:
- Top rectangle: \(27 \, \text{yd} \times 16 \, \text{yd}\)
- Bottom rectangle: \(10 \, \text{yd} \times 3 \, \text{yd}\)

#### Area:
The total area is the sum of the areas of the two rectangles.
\[
\text{Area of top rectangle} = 27 \times 16 = 432 \, \text{yd}^2
\]
\[
\text{Area of bottom rectangle} = 10 \times 3 = 30 \, \text{yd}^2
\]
\[
\text{Total Area} = 432 + 30 = 462 \, \text{yd}^2
\]

#### Perimeter:
The perimeter is the sum of all the outer edges.
\[
\text{Perimeter} = 27 + 16 + 10 + 3 + 24 + 24 = 104 \, \text{yd}
\]
(Note: The horizontal gap between the two rectangles is \(27 - 10 = 17 \, \text{yd}\), so the total horizontal length is \(16 + 17 + 3 = 36 \, \text{yd}\). The vertical sides are \(27\) and \(10\), and the remaining sides are \(16\) and \(3\).)

---

Shape 6:

#### Dimensions:
- Rectangle: \(34 \, \text{yd} \times 9 \, \text{yd}\)

#### Area:
\[
\text{Area} = 34 \times 9 = 306 \, \text{yd}^2
\]

#### Perimeter:
\[
\text{Perimeter} = 2 \times (\text{length} + \text{width}) = 2 \times (34 + 9) = 2 \times 43 = 86 \, \text{yd}
\]

---

Shape 7:

#### Dimensions:
- Top rectangle: \(38 \, \text{in} \times 9 \, \text{in}\)
- Bottom rectangle: \(15 \, \text{in} \times 4 \, \text{in}\)

#### Area:
The total area is the sum of the areas of the two rectangles.
\[
\text{Area of top rectangle} = 38 \times 9 = 342 \, \text{in}^2
\]
\[
\text{Area of bottom rectangle} = 15 \times 4 = 60 \, \text{in}^2
\]
\[
\text{Total Area} = 342 + 60 = 402 \, \text{in}^2
\]

#### Perimeter:
The perimeter is the sum of all the outer edges.
\[
\text{Perimeter} = 38 + 9 + 15 + 4 + 29 + 29 = 124 \, \text{in}
\]
(Note: The horizontal gap between the two rectangles is \(38 - 15 = 23 \, \text{in}\), so the total horizontal length is \(9 + 23 + 4 = 36 \, \text{in}\). The vertical sides are \(38\) and \(15\), and the remaining sides are \(9\) and \(4\).)

---

Shape 8:

#### Dimensions:
- Main rectangle: \(26 \, \text{yd} \times 48 \, \text{yd}\)
- Small rectangle: \(11 \, \text{yd} \times 24 \, \text{yd}\)

#### Area:
The total area is the area of the main rectangle minus the area of the small rectangle.
\[
\text{Area of main rectangle} = 26 \times 48 = 1248 \, \text{yd}^2
\]
\[
\text{Area of small rectangle} = 11 \times 24 = 264 \, \text{yd}^2
\]
\[
\text{Total Area} = 1248 - 264 = 984 \, \text{yd}^2
\]

#### Perimeter:
The perimeter is the sum of all the outer edges.
\[
\text{Perimeter} = 26 + 48 + 26 + 48 = 148 \, \text{yd}
\]
(Note: The small rectangle does not affect the outer perimeter.)

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
\text{Shape 1:} & \text{Area} = 415 \, \text{in}^2, \, \text{Perimeter} = 88 \, \text{in} \\
\text{Shape 2:} & \text{Area} = 705 \, \text{in}^2, \, \text{Perimeter} = 121 \, \text{in} \\
\text{Shape 3:} & \text{Area} = 180 \, \text{in}^2, \, \text{Perimeter} = 70 \, \text{in} \\
\text{Shape 4:} & \text{Area} = 779 \, \text{ft}^2, \, \text{Perimeter} = 128 \, \text{ft} \\
\text{Shape 5:} & \text{Area} = 462 \, \text{yd}^2, \, \text{Perimeter} = 104 \, \text{yd} \\
\text{Shape 6:} & \text{Area} = 306 \, \text{yd}^2, \, \text{Perimeter} = 86 \, \text{yd} \\
\text{Shape 7:} & \text{Area} = 402 \, \text{in}^2, \, \text{Perimeter} = 124 \, \text{in} \\
\text{Shape 8:} & \text{Area} = 984 \, \text{yd}^2, \, \text{Perimeter} = 148 \, \text{yd} \\
\end{array}
}
\]