Grade 5 Area & Perimeter Worksheet featuring problems on calculating area and perimeter of squares, rectangles, and triangles with labeled dimensions.

To solve the problems in the "Area & Perimeter" worksheet, we need to use the formulas for calculating the area and perimeter of different shapes. Let's go through each problem step by step.

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1. Square (Side = 11 m)

#### Area of a Square:
\[ \text{Area} = \text{side}^2 \]
\[ \text{Area} = 11^2 = 121 \, \text{m}^2 \]

#### Perimeter of a Square:
\[ \text{Perimeter} = 4 \times \text{side} \]
\[ \text{Perimeter} = 4 \times 11 = 44 \, \text{m} \]

Answer:
- Area: \( 121 \, \text{m}^2 \)
- Perimeter: \( 44 \, \text{m} \)

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2. Rectangle (Length = 12 m, Width = 5 m)

#### Area of a Rectangle:
\[ \text{Area} = \text{length} \times \text{width} \]
\[ \text{Area} = 12 \times 5 = 60 \, \text{m}^2 \]

#### Perimeter of a Rectangle:
\[ \text{Perimeter} = 2 \times (\text{length} + \text{width}) \]
\[ \text{Perimeter} = 2 \times (12 + 5) = 2 \times 17 = 34 \, \text{m} \]

Answer:
- Area: \( 60 \, \text{m}^2 \)
- Perimeter: \( 34 \, \text{m} \)

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3. Triangle (Base = 12 m, Height = 10 m)

#### Area of a Triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
\[ \text{Area} = \frac{1}{2} \times 12 \times 10 = 6 \times 10 = 60 \, \text{m}^2 \]

(Note: The perimeter of a triangle cannot be calculated without knowing all three sides. Since only the base and height are given, we can only calculate the area.)

Answer:
- Area: \( 60 \, \text{m}^2 \)

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4. Square (Side = 5 m)

#### Area of a Square:
\[ \text{Area} = \text{side}^2 \]
\[ \text{Area} = 5^2 = 25 \, \text{m}^2 \]

#### Perimeter of a Square:
\[ \text{Perimeter} = 4 \times \text{side} \]
\[ \text{Perimeter} = 4 \times 5 = 20 \, \text{m} \]

Answer:
- Area: \( 25 \, \text{m}^2 \)
- Perimeter: \( 20 \, \text{m} \)

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5. Triangle (Base = 8 m, Height = 7 m)

#### Area of a Triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
\[ \text{Area} = \frac{1}{2} \times 8 \times 7 = 4 \times 7 = 28 \, \text{m}^2 \]

(Note: The perimeter of a triangle cannot be calculated without knowing all three sides. Since only the base and height are given, we can only calculate the area.)

Answer:
- Area: \( 28 \, \text{m}^2 \)

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6. Rectangle (Length = 9 m, Width = 3 m)

#### Area of a Rectangle:
\[ \text{Area} = \text{length} \times \text{width} \]
\[ \text{Area} = 9 \times 3 = 27 \, \text{m}^2 \]

#### Perimeter of a Rectangle:
\[ \text{Perimeter} = 2 \times (\text{length} + \text{width}) \]
\[ \text{Perimeter} = 2 \times (9 + 3) = 2 \times 12 = 24 \, \text{m} \]

Answer:
- Area: \( 27 \, \text{m}^2 \)
- Perimeter: \( 24 \, \text{m} \)

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7. Square (Side = 9 m)

#### Area of a Square:
\[ \text{Area} = \text{side}^2 \]
\[ \text{Area} = 9^2 = 81 \, \text{m}^2 \]

#### Perimeter of a Square:
\[ \text{Perimeter} = 4 \times \text{side} \]
\[ \text{Perimeter} = 4 \times 9 = 36 \, \text{m} \]

Answer:
- Area: \( 81 \, \text{m}^2 \)
- Perimeter: \( 36 \, \text{m} \)

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8. Triangle (Base = 10 m, Height = 6 m)

#### Area of a Triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
\[ \text{Area} = \frac{1}{2} \times 10 \times 6 = 5 \times 6 = 30 \, \text{m}^2 \]

(Note: The perimeter of a triangle cannot be calculated without knowing all three sides. Since only the base and height are given, we can only calculate the area.)

Answer:
- Area: \( 30 \, \text{m}^2 \)

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Final Answers:

1. Square (11 m):
- Area: \( \boxed{121 \, \text{m}^2} \)
- Perimeter: \( \boxed{44 \, \text{m}} \)

2. Rectangle (12 m × 5 m):
- Area: \( \boxed{60 \, \text{m}^2} \)
- Perimeter: \( \boxed{34 \, \text{m}} \)

3. Triangle (Base = 12 m, Height = 10 m):
- Area: \( \boxed{60 \, \text{m}^2} \)

4. Square (5 m):
- Area: \( \boxed{25 \, \text{m}^2} \)
- Perimeter: \( \boxed{20 \, \text{m}} \)

5. Triangle (Base = 8 m, Height = 7 m):
- Area: \( \boxed{28 \, \text{m}^2} \)

6. Rectangle (9 m × 3 m):
- Area: \( \boxed{27 \, \text{m}^2} \)
- Perimeter: \( \boxed{24 \, \text{m}} \)

7. Square (9 m):
- Area: \( \boxed{81 \, \text{m}^2} \)
- Perimeter: \( \boxed{36 \, \text{m}} \)

8. Triangle (Base = 10 m, Height = 6 m):
- Area: \( \boxed{30 \, \text{m}^2} \)