Area and Perimeter of Triangles Worksheet | StudyX - Free Printable

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

---

Triangle 1

#### Dimensions:
- Base = 12 ft
- Height = 6 ft
- One side = 8 ft (hypotenuse of the right triangle)

#### Area:
The formula for the area of a triangle is:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
\[
\text{Area} = \frac{1}{2} \times 12 \times 6 = 36 \text{ square feet}
\]

#### Perimeter:
To find the perimeter, we need the length of the third side. Since it is a right triangle, we can use the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
Here, \(a = 6\) ft, \(b = 8\) ft, and \(c\) is the hypotenuse.
\[
6^2 + 8^2 = c^2
\]
\[
36 + 64 = c^2
\]
\[
100 = c^2 \implies c = 10 \text{ ft}
\]
Now, the perimeter is:
\[
\text{Perimeter} = 12 + 6 + 10 = 28 \text{ feet}
\]

#### Final Answers for Triangle 1:
\[
\text{Area} = 36 \text{ square feet}, \quad \text{Perimeter} = 28 \text{ feet}
\]

---

Triangle 2

#### Dimensions:
- Base = 25 ft
- Height = 12 ft
- One side = 15 ft
- Hypotenuse = 20 ft

#### Area:
Using the area formula:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
\[
\text{Area} = \frac{1}{2} \times 25 \times 12 = 150 \text{ square feet}
\]

#### Perimeter:
The perimeter is the sum of all sides:
\[
\text{Perimeter} = 25 + 15 + 20 = 60 \text{ feet}
\]

#### Final Answers for Triangle 2:
\[
\text{Area} = 150 \text{ square feet}, \quad \text{Perimeter} = 60 \text{ feet}
\]

---

Triangle 3

#### Dimensions:
- Base = 6 m
- Height = 8 m
- Two equal sides = 10 m each

#### Area:
Using the area formula:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
\[
\text{Area} = \frac{1}{2} \times 6 \times 8 = 24 \text{ square meters}
\]

#### Perimeter:
The perimeter is the sum of all sides:
\[
\text{Perimeter} = 6 + 10 + 10 = 26 \text{ meters}
\]

#### Final Answers for Triangle 3:
\[
\text{Area} = 24 \text{ square meters}, \quad \text{Perimeter} = 26 \text{ meters}
\]

---

Triangle 4

#### Dimensions:
- Base = 12 cm
- Height = 5 cm
- One side = 8 cm
- Another side = 6 cm

#### Area:
Using the area formula:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
\[
\text{Area} = \frac{1}{2} \times 12 \times 5 = 30 \text{ square centimeters}
\]

#### Perimeter:
To find the perimeter, we need the length of the hypotenuse. Using the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
Here, \(a = 5\) cm, \(b = 12\) cm, and \(c\) is the hypotenuse.
\[
5^2 + 12^2 = c^2
\]
\[
25 + 144 = c^2
\]
\[
169 = c^2 \implies c = 13 \text{ cm}
\]
Now, the perimeter is:
\[
\text{Perimeter} = 12 + 5 + 13 = 30 \text{ cm}
\]

#### Final Answers for Triangle 4:
\[
\text{Area} = 30 \text{ square centimeters}, \quad \text{Perimeter} = 30 \text{ cm}
\]

---

Triangle 5

#### Dimensions:
- Base = 6 cm
- Height = 3 cm
- One side = 7 cm
- Another side = 3 cm

#### Area:
Using the area formula:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
\[
\text{Area} = \frac{1}{2} \times 6 \times 3 = 9 \text{ square centimeters}
\]

#### Perimeter:
The perimeter is the sum of all sides:
\[
\text{Perimeter} = 6 + 3 + 7 = 16 \text{ cm}
\]

#### Final Answers for Triangle 5:
\[
\text{Area} = 9 \text{ square centimeters}, \quad \text{Perimeter} = 16 \text{ cm}
\]

---

Triangle 6

#### Dimensions:
- Base = 12 m
- Height = 16 m
- Hypotenuse = 18 m

#### Area:
Using the area formula:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
\[
\text{Area} = \frac{1}{2} \times 12 \times 16 = 96 \text{ square meters}
\]

#### Perimeter:
The perimeter is the sum of all sides:
\[
\text{Perimeter} = 12 + 16 + 18 = 46 \text{ meters}
\]

#### Final Answers for Triangle 6:
\[
\text{Area} = 96 \text{ square meters}, \quad \text{Perimeter} = 46 \text{ meters}
\]

---

Final Answer Summary:

1. \(\text{Area} = 36 \text{ square feet}, \quad \text{Perimeter} = 28 \text{ feet}\)
2. \(\text{Area} = 150 \text{ square feet}, \quad \text{Perimeter} = 60 \text{ feet}\)
3. \(\text{Area} = 24 \text{ square meters}, \quad \text{Perimeter} = 26 \text{ meters}\)
4. \(\text{Area} = 30 \text{ square centimeters}, \quad \text{Perimeter} = 30 \text{ cm}\)
5. \(\text{Area} = 9 \text{ square centimeters}, \quad \text{Perimeter} = 16 \text{ cm}\)
6. \(\text{Area} = 96 \text{ square meters}, \quad \text{Perimeter} = 46 \text{ meters}\)

\[
\boxed{
\begin{array}{ll}
\text{Triangle 1:} & \text{Area} = 36 \text{ square feet}, \quad \text{Perimeter} = 28 \text{ feet} \\
\text{Triangle 2:} & \text{Area} = 150 \text{ square feet}, \quad \text{Perimeter} = 60 \text{ feet} \\
\text{Triangle 3:} & \text{Area} = 24 \text{ square meters}, \quad \text{Perimeter} = 26 \text{ meters} \\
\text{Triangle 4:} & \text{Area} = 30 \text{ square centimeters}, \quad \text{Perimeter} = 30 \text{ cm} \\
\text{Triangle 5:} & \text{Area} = 9 \text{ square centimeters}, \quad \text{Perimeter} = 16 \text{ cm} \\
\text{Triangle 6:} & \text{Area} = 96 \text{ square meters}, \quad \text{Perimeter} = 46 \text{ meters} \\
\end{array}
}
\]