Finding Area and Perimeter if Irregular Polygons Worksheet | Live ... - Free Printable

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

---

Problem 1

Shape:
- A rectangle with dimensions \(10 \, \text{cm} \times 18 \, \text{cm}\), but with a smaller rectangle cut out (\(4 \, \text{cm} \times 8 \, \text{cm}\)).

#### Area:
1. Calculate the area of the large rectangle:
\[
\text{Area}_{\text{large}} = 10 \times 18 = 180 \, \text{cm}^2
\]
2. Calculate the area of the smaller rectangle:
\[
\text{Area}_{\text{small}} = 4 \times 8 = 32 \, \text{cm}^2
\]
3. Subtract the area of the smaller rectangle from the area of the larger rectangle:
\[
\text{Area}_{\text{total}} = 180 - 32 = 148 \, \text{cm}^2
\]

#### Perimeter:
1. The perimeter is the sum of all outer sides. Counting the sides:
\[
\text{Perimeter} = 10 + 18 + 10 + 18 + 4 + 4 = 64 \, \text{cm}
\]

Answer:
\[
\boxed{148 \, \text{cm}^2, 64 \, \text{cm}}
\]

---

Problem 2

Shape:
- A rectangle with a smaller rectangle cut out in the middle.

#### Area:
1. Calculate the area of the large rectangle:
\[
\text{Area}_{\text{large}} = 8.5 \times 6 = 51 \, \text{in}^2
\]
2. Calculate the area of the smaller rectangle:
\[
\text{Area}_{\text{small}} = 2.5 \times 6 = 15 \, \text{in}^2
\]
3. Subtract the area of the smaller rectangle from the area of the larger rectangle:
\[
\text{Area}_{\text{total}} = 51 - 15 = 36 \, \text{in}^2
\]

#### Perimeter:
1. The perimeter is the sum of all outer sides. Counting the sides:
\[
\text{Perimeter} = 8.5 + 6 + 8.5 + 6 + 4 + 4 = 37 \, \text{in}
\]

Answer:
\[
\boxed{36 \, \text{in}^2, 37 \, \text{in}}
\]

---

Problem 3

Shape:
- An L-shaped polygon.

#### Area:
1. Break the shape into two rectangles:
- Rectangle 1: \(19 \, \text{in} \times 7 \, \text{in}\)
- Rectangle 2: \(12 \, \text{in} \times 6 \, \text{in}\)
2. Calculate the area of each rectangle:
\[
\text{Area}_{\text{rect1}} = 19 \times 7 = 133 \, \text{in}^2
\]
\[
\text{Area}_{\text{rect2}} = 12 \times 6 = 72 \, \text{in}^2
\]
3. Add the areas of the two rectangles:
\[
\text{Area}_{\text{total}} = 133 + 72 = 205 \, \text{in}^2
\]

#### Perimeter:
1. Count all the outer sides:
\[
\text{Perimeter} = 19 + 7 + 12 + 6 + 7 + 12 = 63 \, \text{in}
\]

Answer:
\[
\boxed{205 \, \text{in}^2, 63 \, \text{in}}
\]

---

Problem 4

Shape:
- An L-shaped polygon.

#### Area:
1. Break the shape into two rectangles:
- Rectangle 1: \(16.8 \, \text{ft} \times 8.1 \, \text{ft}\)
- Rectangle 2: \(13.2 \, \text{ft} \times 5.1 \, \text{ft}\)
2. Calculate the area of each rectangle:
\[
\text{Area}_{\text{rect1}} = 16.8 \times 8.1 = 136.08 \, \text{ft}^2
\]
\[
\text{Area}_{\text{rect2}} = 13.2 \times 5.1 = 67.32 \, \text{ft}^2
\]
3. Add the areas of the two rectangles:
\[
\text{Area}_{\text{total}} = 136.08 + 67.32 = 203.4 \, \text{ft}^2
\]

#### Perimeter:
1. Count all the outer sides:
\[
\text{Perimeter} = 16.8 + 8.1 + 13.2 + 5.1 + 4.4 + 12.4 = 59.0 \, \text{ft}
\]

Answer:
\[
\boxed{203.4 \, \text{ft}^2, 59.0 \, \text{ft}}
\]

---

Problem 5

Shape:
- An L-shaped polygon.

#### Area:
1. Break the shape into two rectangles:
- Rectangle 1: \(17.8 \, \text{in} \times 6.5 \, \text{in}\)
- Rectangle 2: \(15.2 \, \text{in} \times 4.8 \, \text{in}\)
2. Calculate the area of each rectangle:
\[
\text{Area}_{\text{rect1}} = 17.8 \times 6.5 = 115.7 \, \text{in}^2
\]
\[
\text{Area}_{\text{rect2}} = 15.2 \times 4.8 = 72.96 \, \text{in}^2
\]
3. Add the areas of the two rectangles:
\[
\text{Area}_{\text{total}} = 115.7 + 72.96 = 188.66 \, \text{in}^2
\]

#### Perimeter:
1. Count all the outer sides:
\[
\text{Perimeter} = 17.8 + 6.5 + 15.2 + 4.8 + 5.7 + 17.8 = 67.8 \, \text{in}
\]

Answer:
\[
\boxed{188.66 \, \text{in}^2, 67.8 \, \text{in}}
\]

---

Problem 6

Shape:
- An L-shaped polygon.

#### Area:
1. Break the shape into two rectangles:
- Rectangle 1: \(25.5 \, \text{ft} \times 18.8 \, \text{ft}\)
- Rectangle 2: \(25.5 \, \text{ft} \times 4.2 \, \text{ft}\)
2. Calculate the area of each rectangle:
\[
\text{Area}_{\text{rect1}} = 25.5 \times 18.8 = 478.2 \, \text{ft}^2
\]
\[
\text{Area}_{\text{rect2}} = 25.5 \times 4.2 = 107.1 \, \text{ft}^2
\]
3. Add the areas of the two rectangles:
\[
\text{Area}_{\text{total}} = 478.2 + 107.1 = 585.3 \, \text{ft}^2
\]

#### Perimeter:
1. Count all the outer sides:
\[
\text{Perimeter} = 25.5 + 18.8 + 25.5 + 4.2 + 5.5 + 25.5 = 105.0 \, \text{ft}
\]

Answer:
\[
\boxed{585.3 \, \text{ft}^2, 105.0 \, \text{ft}}
\]

---

Problem 7

Shape:
- An L-shaped polygon.

#### Area:
1. Break the shape into three rectangles:
- Rectangle 1: \(16 \, \text{cm} \times 9 \, \text{cm}\)
- Rectangle 2: \(16 \, \text{cm} \times 6.8 \, \text{cm}\)
- Rectangle 3: \(5.5 \, \text{cm} \times 6.8 \, \text{cm}\)
2. Calculate the area of each rectangle:
\[
\text{Area}_{\text{rect1}} = 16 \times 9 = 144 \, \text{cm}^2
\]
\[
\text{Area}_{\text{rect2}} = 16 \times 6.8 = 108.8 \, \text{cm}^2
\]
\[
\text{Area}_{\text{rect3}} = 5.5 \times 6.8 = 37.4 \, \text{cm}^2
\]
3. Add the areas of the three rectangles:
\[
\text{Area}_{\text{total}} = 144 + 108.8 + 37.4 = 290.2 \, \text{cm}^2
\]

#### Perimeter:
1. Count all the outer sides:
\[
\text{Perimeter} = 16 + 9 + 16 + 6.8 + 5.5 + 6.8 + 16 + 9 = 75.1 \, \text{cm}
\]

Answer:
\[
\boxed{290.2 \, \text{cm}^2, 75.1 \, \text{cm}}
\]

---

Problem 8

Shape:
- An L-shaped polygon.

#### Area:
1. Break the shape into three rectangles:
- Rectangle 1: \(16.8 \, \text{m} \times 3.8 \, \text{m}\)
- Rectangle 2: \(16.8 \, \text{m} \times 3.8 \, \text{m}\)
- Rectangle 3: \(8.8 \, \text{m} \times 4.4 \, \text{m}\)
2. Calculate the area of each rectangle:
\[
\text{Area}_{\text{rect1}} = 16.8 \times 3.8 = 63.84 \, \text{m}^2
\]
\[
\text{Area}_{\text{rect2}} = 16.8 \times 3.8 = 63.84 \, \text{m}^2
\]
\[
\text{Area}_{\text{rect3}} = 8.8 \times 4.4 = 38.72 \, \text{m}^2
\]
3. Add the areas of the three rectangles:
\[
\text{Area}_{\text{total}} = 63.84 + 63.84 + 38.72 = 166.4 \, \text{m}^2
\]

#### Perimeter:
1. Count all the outer sides:
\[
\text{Perimeter} = 16.8 + 3.8 + 16.8 + 3.8 + 8.8 + 4.4 + 4.4 + 8.8 = 63.6 \, \text{m}
\]

Answer:
\[
\boxed{166.4 \, \text{m}^2, 63.6 \, \text{m}}
\]

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Final Answers:

1. \(\boxed{148 \, \text{cm}^2, 64 \, \text{cm}}\)
2. \(\boxed{36 \, \text{in}^2, 37 \, \text{in}}\)
3. \(\boxed{205 \, \text{in}^2, 63 \, \text{in}}\)
4. \(\boxed{203.4 \, \text{ft}^2, 59.0 \, \text{ft}}\)
5. \(\boxed{188.66 \, \text{in}^2, 67.8 \, \text{in}}\)
6. \(\boxed{585.3 \, \text{ft}^2, 105.0 \, \text{ft}}\)
7. \(\boxed{290.2 \, \text{cm}^2, 75.1 \, \text{cm}}\)
8. \(\boxed{166.4 \, \text{m}^2, 63.6 \, \text{m}}\)