Grade 5 Area and Perimeter Worksheets | Free Math Worksheets - 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 a smaller rectangle cut out.

Dimensions:
- Outer rectangle: \(18 \, \text{cm} \times 10 \, \text{cm}\)
- Inner rectangle: \(4 \, \text{cm} \times 8 \, \text{cm}\)

#### Area:
1. Area of the outer rectangle:
\[
\text{Area}_{\text{outer}} = 18 \times 10 = 180 \, \text{cm}^2
\]
2. Area of the inner rectangle:
\[
\text{Area}_{\text{inner}} = 4 \times 8 = 32 \, \text{cm}^2
\]
3. Total area:
\[
\text{Area} = \text{Area}_{\text{outer}} - \text{Area}_{\text{inner}} = 180 - 32 = 148 \, \text{cm}^2
\]

#### Perimeter:
1. The perimeter is the sum of all outer edges. Since the inner rectangle does not affect the outer perimeter:
\[
\text{Perimeter} = 2 \times (18 + 10) = 2 \times 28 = 56 \, \text{cm}
\]

Answer:
\[
\boxed{148 \, \text{cm}^2, 56 \, \text{cm}}
\]

---

Problem 2

Shape:
- Two rectangles side by side with a smaller rectangle in the middle.

Dimensions:
- Left rectangle: \(4 \, \text{in} \times 8.5 \, \text{in}\)
- Right rectangle: \(4 \, \text{in} \times 8.5 \, \text{in}\)
- Middle rectangle (cutout): \(2.5 \, \text{in} \times 6 \, \text{in}\)

#### Area:
1. Area of the left rectangle:
\[
\text{Area}_{\text{left}} = 4 \times 8.5 = 34 \, \text{in}^2
\]
2. Area of the right rectangle:
\[
\text{Area}_{\text{right}} = 4 \times 8.5 = 34 \, \text{in}^2
\]
3. Area of the middle rectangle (cutout):
\[
\text{Area}_{\text{middle}} = 2.5 \times 6 = 15 \, \text{in}^2
\]
4. Total area:
\[
\text{Area} = \text{Area}_{\text{left}} + \text{Area}_{\text{right}} - \text{Area}_{\text{middle}} = 34 + 34 - 15 = 53 \, \text{in}^2
\]

#### Perimeter:
1. The perimeter includes all outer edges. The total length of the top and bottom edges is:
\[
4 + 2.5 + 4 = 10.5 \, \text{in}
\]
2. The total length of the left and right edges is:
\[
8.5 + 8.5 = 17 \, \text{in}
\]
3. Total perimeter:
\[
\text{Perimeter} = 2 \times (10.5 + 8.5) = 2 \times 19 = 38 \, \text{in}
\]

Answer:
\[
\boxed{53 \, \text{in}^2, 38 \, \text{in}}
\]

---

Problem 3

Shape:
- An L-shaped polygon.

Dimensions:
- Top part: \(12 \, \text{in} \times 7 \, \text{in}\)
- Bottom part: \(6 \, \text{in} \times 19 \, \text{in}\)

#### Area:
1. Area of the top rectangle:
\[
\text{Area}_{\text{top}} = 12 \times 7 = 84 \, \text{in}^2
\]
2. Area of the bottom rectangle:
\[
\text{Area}_{\text{bottom}} = 6 \times 19 = 114 \, \text{in}^2
\]
3. Total area:
\[
\text{Area} = \text{Area}_{\text{top}} + \text{Area}_{\text{bottom}} = 84 + 114 = 208 \, \text{in}^2
\]

#### Perimeter:
1. The perimeter includes all outer edges. The total length of the top and bottom edges is:
\[
12 + 6 + 19 = 37 \, \text{in}
\]
2. The total length of the left and right edges is:
\[
7 + 19 = 26 \, \text{in}
\]
3. Total perimeter:
\[
\text{Perimeter} = 37 + 26 = 63 \, \text{in}
\]

Answer:
\[
\boxed{208 \, \text{in}^2, 63 \, \text{in}}
\]

---

Problem 4

Shape:
- An irregular polygon with multiple sides.

Dimensions:
- Top: \(16.8 \, \text{ft}\)
- Right: \(13.2 \, \text{ft}\)
- Bottom: \(12.4 \, \text{ft}\)
- Left: \(8.1 \, \text{ft}\)
- Inner dimensions: \(4.4 \, \text{ft}\) and \(5.1 \, \text{ft}\)

#### Area:
1. Break the shape into two rectangles:
- Rectangle 1: \(16.8 \, \text{ft} \times 8.1 \, \text{ft}\)
- Rectangle 2: \(12.4 \, \text{ft} \times 4.4 \, \text{ft}\)
2. Area of Rectangle 1:
\[
\text{Area}_{1} = 16.8 \times 8.1 = 136.08 \, \text{ft}^2
\]
3. Area of Rectangle 2:
\[
\text{Area}_{2} = 12.4 \times 4.4 = 54.56 \, \text{ft}^2
\]
4. Total area:
\[
\text{Area} = \text{Area}_{1} + \text{Area}_{2} = 136.08 + 54.56 = 190.64 \, \text{ft}^2
\]

#### Perimeter:
1. Sum all the outer edges:
\[
\text{Perimeter} = 16.8 + 13.2 + 12.4 + 8.1 + 4.4 + 5.1 = 60 \, \text{ft}
\]

Answer:
\[
\boxed{190.64 \, \text{ft}^2, 60 \, \text{ft}}
\]

---

Problem 5

Shape:
- An irregular polygon with multiple sides.

Dimensions:
- Top: \(17.8 \, \text{in}\)
- Right: \(5.7 \, \text{in}\)
- Bottom: \(15.2 \, \text{in}\)
- Left: \(6.5 \, \text{in}\)
- Inner dimension: \(4.8 \, \text{in}\)

#### 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. Area of Rectangle 1:
\[
\text{Area}_{1} = 17.8 \times 6.5 = 115.7 \, \text{in}^2
\]
3. Area of Rectangle 2:
\[
\text{Area}_{2} = 15.2 \times 4.8 = 72.96 \, \text{in}^2
\]
4. Total area:
\[
\text{Area} = \text{Area}_{1} + \text{Area}_{2} = 115.7 + 72.96 = 188.66 \, \text{in}^2
\]

#### Perimeter:
1. Sum all the outer edges:
\[
\text{Perimeter} = 17.8 + 5.7 + 15.2 + 6.5 + 4.8 = 49 \, \text{in}
\]

Answer:
\[
\boxed{188.66 \, \text{in}^2, 49 \, \text{in}}
\]

---

Problem 6

Shape:
- An irregular polygon with multiple sides.

Dimensions:
- Top: \(18.8 \, \text{ft}\)
- Right: \(25.5 \, \text{ft}\)
- Bottom: \(18.8 \, \text{ft}\)
- Left: \(5.5 \, \text{ft}\)
- Inner dimension: \(4.2 \, \text{ft}\)

#### Area:
1. Break the shape into two rectangles:
- Rectangle 1: \(18.8 \, \text{ft} \times 5.5 \, \text{ft}\)
- Rectangle 2: \(18.8 \, \text{ft} \times 4.2 \, \text{ft}\)
2. Area of Rectangle 1:
\[
\text{Area}_{1} = 18.8 \times 5.5 = 103.4 \, \text{ft}^2
\]
3. Area of Rectangle 2:
\[
\text{Area}_{2} = 18.8 \times 4.2 = 79.36 \, \text{ft}^2
\]
4. Total area:
\[
\text{Area} = \text{Area}_{1} + \text{Area}_{2} = 103.4 + 79.36 = 182.76 \, \text{ft}^2
\]

#### Perimeter:
1. Sum all the outer edges:
\[
\text{Perimeter} = 18.8 + 25.5 + 18.8 + 5.5 + 4.2 + 4.2 = 77 \, \text{ft}
\]

Answer:
\[
\boxed{182.76 \, \text{ft}^2, 77 \, \text{ft}}
\]

---

Problem 7

Shape:
- An irregular polygon with multiple sides.

Dimensions:
- Top: \(9 \, \text{cm}\)
- Right: \(6.8 \, \text{cm}\)
- Bottom: \(16 \, \text{cm}\)
- Left: \(6.8 \, \text{cm}\)
- Inner dimensions: \(5.5 \, \text{cm}\) and \(6.8 \, \text{cm}\)

#### Area:
1. Break the shape into two rectangles:
- Rectangle 1: \(9 \, \text{cm} \times 6.8 \, \text{cm}\)
- Rectangle 2: \(16 \, \text{cm} \times 6.8 \, \text{cm}\)
2. Area of Rectangle 1:
\[
\text{Area}_{1} = 9 \times 6.8 = 61.2 \, \text{cm}^2
\]
3. Area of Rectangle 2:
\[
\text{Area}_{2} = 16 \times 6.8 = 108.8 \, \text{cm}^2
\]
4. Total area:
\[
\text{Area} = \text{Area}_{1} + \text{Area}_{2} = 61.2 + 108.8 = 170 \, \text{cm}^2
\]

#### Perimeter:
1. Sum all the outer edges:
\[
\text{Perimeter} = 9 + 6.8 + 16 + 6.8 + 5.5 + 6.8 = 50.9 \, \text{cm}
\]

Answer:
\[
\boxed{170 \, \text{cm}^2, 50.9 \, \text{cm}}
\]

---

Problem 8

Shape:
- An irregular polygon with multiple sides.

Dimensions:
- Top: \(3.8 \, \text{m}\)
- Right: \(16.8 \, \text{m}\)
- Bottom: \(3.8 \, \text{m}\)
- Left: \(4.4 \, \text{m}\)
- Inner dimensions: \(4.4 \, \text{m}\), \(8.8 \, \text{m}\), and \(4.4 \, \text{m}\)

#### Area:
1. Break the shape into three rectangles:
- Rectangle 1: \(3.8 \, \text{m} \times 4.4 \, \text{m}\)
- Rectangle 2: \(8.8 \, \text{m} \times 4.4 \, \text{m}\)
- Rectangle 3: \(3.8 \, \text{m} \times 4.4 \, \text{m}\)
2. Area of Rectangle 1:
\[
\text{Area}_{1} = 3.8 \times 4.4 = 16.72 \, \text{m}^2
\]
3. Area of Rectangle 2:
\[
\text{Area}_{2} = 8.8 \times 4.4 = 38.72 \, \text{m}^2
\]
4. Area of Rectangle 3:
\[
\text{Area}_{3} = 3.8 \times 4.4 = 16.72 \, \text{m}^2
\]
5. Total area:
\[
\text{Area} = \text{Area}_{1} + \text{Area}_{2} + \text{Area}_{3} = 16.72 + 38.72 + 16.72 = 72.16 \, \text{m}^2
\]

#### Perimeter:
1. Sum all the outer edges:
\[
\text{Perimeter} = 3.8 + 16.8 + 3.8 + 4.4 + 8.8 + 4.4 = 41.6 \, \text{m}
\]

Answer:
\[
\boxed{72.16 \, \text{m}^2, 41.6 \, \text{m}}
\]

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Final Answers:

1. \(\boxed{148 \, \text{cm}^2, 56 \, \text{cm}}\)
2. \(\boxed{53 \, \text{in}^2, 38 \, \text{in}}\)
3. \(\boxed{208 \, \text{in}^2, 63 \, \text{in}}\)
4. \(\boxed{190.64 \, \text{ft}^2, 60 \, \text{ft}}\)
5. \(\boxed{188.66 \, \text{in}^2, 49 \, \text{in}}\)
6. \(\boxed{182.76 \, \text{ft}^2, 77 \, \text{ft}}\)
7. \(\boxed{170 \, \text{cm}^2, 50.9 \, \text{cm}}\)
8. \(\boxed{72.16 \, \text{m}^2, 41.6 \, \text{m}}\)