Area and Perimeter of Triangles Worksheets - Math Monks - Free Printable

To solve the problem, we need to calculate the area and perimeter of each triangle. Let's go through each triangle step by step.

Formula Recap:

1. Area of a Triangle:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
2. Perimeter of a Triangle:
\[
\text{Perimeter} = \text{side}_1 + \text{side}_2 + \text{side}_3
\]

---

Triangle 1:

- Base: 12 ft
- Height: 6 ft
- Other sides: 8 ft (hypotenuse), 4 ft (one leg)

#### Area:
\[
\text{Area} = \frac{1}{2} \times 12 \times 6 = \frac{1}{2} \times 72 = 36 \text{ ft}^2
\]

#### Perimeter:
\[
\text{Perimeter} = 12 + 8 + 4 = 24 \text{ ft}
\]

---

Triangle 2:

- Base: 25 ft
- Height: 12 ft
- Other sides: 15 ft, 20 ft

#### Area:
\[
\text{Area} = \frac{1}{2} \times 25 \times 12 = \frac{1}{2} \times 300 = 150 \text{ ft}^2
\]

#### Perimeter:
\[
\text{Perimeter} = 25 + 15 + 20 = 60 \text{ ft}
\]

---

Triangle 3:

- Base: 6 m
- Height: 8 m
- Other sides: 10 m (hypotenuse), 10 m (equal sides)

#### Area:
\[
\text{Area} = \frac{1}{2} \times 6 \times 8 = \frac{1}{2} \times 48 = 24 \text{ m}^2
\]

#### Perimeter:
\[
\text{Perimeter} = 6 + 10 + 10 = 26 \text{ m}
\]

---

Triangle 4:

- Base: 12 cm
- Height: 6 cm
- Other sides: 8 cm, 5 cm

#### Area:
\[
\text{Area} = \frac{1}{2} \times 12 \times 6 = \frac{1}{2} \times 72 = 36 \text{ cm}^2
\]

#### Perimeter:
\[
\text{Perimeter} = 12 + 8 + 5 = 25 \text{ cm}
\]

---

Triangle 5:

- Base: 6 cm
- Height: 7 cm
- Other sides: 3 cm, 3 cm (isosceles triangle)

#### Area:
\[
\text{Area} = \frac{1}{2} \times 6 \times 7 = \frac{1}{2} \times 42 = 21 \text{ cm}^2
\]

#### Perimeter:
\[
\text{Perimeter} = 6 + 3 + 3 = 12 \text{ cm}
\]

---

Triangle 6:

- Base: 12 m
- Height: 16 m
- Other sides: 18 m (hypotenuse)

#### Area:
\[
\text{Area} = \frac{1}{2} \times 12 \times 16 = \frac{1}{2} \times 192 = 96 \text{ m}^2
\]

#### Perimeter:
\[
\text{Perimeter} = 12 + 16 + 18 = 46 \text{ m}
\]

---

Triangle 7:

- Base: 2.2 yd
- Height: 1.5 yd
- Other sides: 2.5 yd, 3.3 yd

#### Area:
\[
\text{Area} = \frac{1}{2} \times 2.2 \times 1.5 = \frac{1}{2} \times 3.3 = 1.65 \text{ yd}^2
\]

#### Perimeter:
\[
\text{Perimeter} = 2.2 + 2.5 + 3.3 = 8 \text{ yd}
\]

---

Triangle 8:

- Base: 8 yd
- Height: 6 yd
- Other sides: 10 yd (hypotenuse)

#### Area:
\[
\text{Area} = \frac{1}{2} \times 8 \times 6 = \frac{1}{2} \times 48 = 24 \text{ yd}^2
\]

#### Perimeter:
\[
\text{Perimeter} = 8 + 6 + 10 = 24 \text{ yd}
\]

---

Final Answers:

1. Area: 36 ft², Perimeter: 24 ft
2. Area: 150 ft², Perimeter: 60 ft
3. Area: 24 m², Perimeter: 26 m
4. Area: 36 cm², Perimeter: 25 cm
5. Area: 21 cm², Perimeter: 12 cm
6. Area: 96 m², Perimeter: 46 m
7. Area: 1.65 yd², Perimeter: 8 yd
8. Area: 24 yd², Perimeter: 24 yd

\boxed{
\begin{array}{ll}
\text{1. Area: } 36 \text{ ft}^2, & \text{Perimeter: } 24 \text{ ft} \\
\text{2. Area: } 150 \text{ ft}^2, & \text{Perimeter: } 60 \text{ ft} \\
\text{3. Area: } 24 \text{ m}^2, & \text{Perimeter: } 26 \text{ m} \\
\text{4. Area: } 36 \text{ cm}^2, & \text{Perimeter: } 25 \text{ cm} \\
\text{5. Area: } 21 \text{ cm}^2, & \text{Perimeter: } 12 \text{ cm} \\
\text{6. Area: } 96 \text{ m}^2, & \text{Perimeter: } 46 \text{ m} \\
\text{7. Area: } 1.65 \text{ yd}^2, & \text{Perimeter: } 8 \text{ yd} \\
\text{8. Area: } 24 \text{ yd}^2, & \text{Perimeter: } 24 \text{ yd} \\
\end{array}
}