Grade 5 Area and Perimeter Worksheets | Free Math Worksheets - Free Printable

To solve the problems in the worksheet, we need to calculate the area and perimeter for each shape provided. Let's go through each problem step by step.

---

1. Triangle

- Given: Base = 30 m, Height = 12 m
- Formula for Area of a Triangle:
\[
\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}
\]
- Calculation:
\[
\text{Area} = \frac{1}{2} \times 30 \times 12 = \frac{1}{2} \times 360 = 180 \, \text{m}^2
\]

- Answer:
\[
\boxed{180 \, \text{m}^2}
\]

---

2. Triangle

- Given: Base = 8 m, Height = 6 m
- Formula for Area of a Triangle:
\[
\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}
\]
- Calculation:
\[
\text{Area} = \frac{1}{2} \times 8 \times 6 = \frac{1}{2} \times 48 = 24 \, \text{m}^2
\]

- Answer:
\[
\boxed{24 \, \text{m}^2}
\]

---

3. Rectangle

- Given: Length = 13 m, Width = 10 m
- Formula for Area of a Rectangle:
\[
\text{Area} = \text{Length} \times \text{Width}
\]
- Calculation:
\[
\text{Area} = 13 \times 10 = 130 \, \text{m}^2
\]

- Formula for Perimeter of a Rectangle:
\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Width})
\]
- Calculation:
\[
\text{Perimeter} = 2 \times (13 + 10) = 2 \times 23 = 46 \, \text{m}
\]

- Answers:
\[
\text{Area} = \boxed{130 \, \text{m}^2}, \quad \text{Perimeter} = \boxed{46 \, \text{m}}
\]

---

4. Square

- Given: Side = 7 m
- Formula for Area of a Square:
\[
\text{Area} = \text{Side}^2
\]
- Calculation:
\[
\text{Area} = 7^2 = 49 \, \text{m}^2
\]

- Formula for Perimeter of a Square:
\[
\text{Perimeter} = 4 \times \text{Side}
\]
- Calculation:
\[
\text{Perimeter} = 4 \times 7 = 28 \, \text{m}
\]

- Answers:
\[
\text{Area} = \boxed{49 \, \text{m}^2}, \quad \text{Perimeter} = \boxed{28 \, \text{m}}
\]

---

5. Square

- Given: Side = 12 m
- Formula for Area of a Square:
\[
\text{Area} = \text{Side}^2
\]
- Calculation:
\[
\text{Area} = 12^2 = 144 \, \text{m}^2
\]

- Formula for Perimeter of a Square:
\[
\text{Perimeter} = 4 \times \text{Side}
\]
- Calculation:
\[
\text{Perimeter} = 4 \times 12 = 48 \, \text{m}
\]

- Answers:
\[
\text{Area} = \boxed{144 \, \text{m}^2}, \quad \text{Perimeter} = \boxed{48 \, \text{m}}
\]

---

6. Triangle

- Given: Base = 20 m, Height = 15 m
- Formula for Area of a Triangle:
\[
\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}
\]
- Calculation:
\[
\text{Area} = \frac{1}{2} \times 20 \times 15 = \frac{1}{2} \times 300 = 150 \, \text{m}^2
\]

- Answer:
\[
\boxed{150 \, \text{m}^2}
\]

---

Final Answers

1. Triangle: Area = \( \boxed{180 \, \text{m}^2} \)
2. Triangle: Area = \( \boxed{24 \, \text{m}^2} \)
3. Rectangle: Area = \( \boxed{130 \, \text{m}^2} \), Perimeter = \( \boxed{46 \, \text{m}} \)
4. Square: Area = \( \boxed{49 \, \text{m}^2} \), Perimeter = \( \boxed{28 \, \text{m}} \)
5. Square: Area = \( \boxed{144 \, \text{m}^2} \), Perimeter = \( \boxed{48 \, \text{m}} \)
6. Triangle: Area = \( \boxed{150 \, \text{m}^2} \)

---

Boxed Final Answer

\[
\boxed{
\begin{aligned}
1. & \, 180 \, \text{m}^2 \\
2. & \, 24 \, \text{m}^2 \\
3. & \, 130 \, \text{m}^2, \, 46 \, \text{m} \\
4. & \, 49 \, \text{m}^2, \, 28 \, \text{m} \\
5. & \, 144 \, \text{m}^2, \, 48 \, \text{m} \\
6. & \, 150 \, \text{m}^2 \\
\end{aligned}
}
\]