Perimeter and area of triangles activity - Free Printable

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

---

1. Orange Triangle

#### Dimensions:
- Sides: 4 cm, 6 cm, 4 cm

#### Perimeter:
The perimeter of a triangle is the sum of its sides.
\[
\text{Perimeter} = 4 + 6 + 4 = 14 \, \text{cm}
\]

#### Area:
The formula for the area of a triangle is:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
Here, the base is 4 cm, and the height is 6 cm (since it forms a right triangle).
\[
\text{Area} = \frac{1}{2} \times 4 \times 6 = \frac{1}{2} \times 24 = 12 \, \text{cm}^2
\]

#### Final Answers:
\[
\text{Perimeter} = 14 \, \text{cm}, \quad \text{Area} = 12 \, \text{cm}^2
\]

---

2. Blue Triangle

#### Dimensions:
- Sides: 3 cm, 6 cm, 8 cm

#### Perimeter:
\[
\text{Perimeter} = 3 + 6 + 8 = 17 \, \text{cm}
\]

#### Area:
We use Heron's formula since this is not a right triangle. Heron's formula is:
\[
\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}
\]
where \( s \) is the semi-perimeter:
\[
s = \frac{a + b + c}{2} = \frac{3 + 6 + 8}{2} = 8.5 \, \text{cm}
\]
Now, substitute into Heron's formula:
\[
\text{Area} = \sqrt{8.5(8.5 - 3)(8.5 - 6)(8.5 - 8)} = \sqrt{8.5 \times 5.5 \times 2.5 \times 0.5}
\]
Calculate step-by-step:
\[
8.5 \times 5.5 = 46.75
\]
\[
2.5 \times 0.5 = 1.25
\]
\[
46.75 \times 1.25 = 58.4375
\]
\[
\text{Area} = \sqrt{58.4375} \approx 7.64 \, \text{cm}^2
\]

#### Final Answers:
\[
\text{Perimeter} = 17 \, \text{cm}, \quad \text{Area} \approx 7.64 \, \text{cm}^2
\]

---

3. Green Triangle

#### Dimensions:
- Sides: 10 cm, 10 cm, 6 cm

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

#### Area:
This is an isosceles triangle. We can use Heron's formula again. First, calculate the semi-perimeter:
\[
s = \frac{10 + 10 + 6}{2} = 13 \, \text{cm}
\]
Now, substitute into Heron's formula:
\[
\text{Area} = \sqrt{13(13 - 10)(13 - 10)(13 - 6)} = \sqrt{13 \times 3 \times 3 \times 7}
\]
Calculate step-by-step:
\[
13 \times 3 = 39
\]
\[
39 \times 3 = 117
\]
\[
117 \times 7 = 819
\]
\[
\text{Area} = \sqrt{819} \approx 28.62 \, \text{cm}^2
\]

#### Final Answers:
\[
\text{Perimeter} = 26 \, \text{cm}, \quad \text{Area} \approx 28.62 \, \text{cm}^2
\]

---

4. Pink Triangle

#### Dimensions:
- Sides: 11 cm, 12 cm, 13 cm

#### Perimeter:
\[
\text{Perimeter} = 11 + 12 + 13 = 36 \, \text{cm}
\]

#### Area:
Use Heron's formula. First, calculate the semi-perimeter:
\[
s = \frac{11 + 12 + 13}{2} = 18 \, \text{cm}
\]
Now, substitute into Heron's formula:
\[
\text{Area} = \sqrt{18(18 - 11)(18 - 12)(18 - 13)} = \sqrt{18 \times 7 \times 6 \times 5}
\]
Calculate step-by-step:
\[
18 \times 7 = 126
\]
\[
126 \times 6 = 756
\]
\[
756 \times 5 = 3780
\]
\[
\text{Area} = \sqrt{3780} \approx 61.48 \, \text{cm}^2
\]

#### Final Answers:
\[
\text{Perimeter} = 36 \, \text{cm}, \quad \text{Area} \approx 61.48 \, \text{cm}^2
\]

---

5. Red Triangle

#### Dimensions:
- Sides: 10 cm, 10 cm, 10 cm (equilateral triangle)
- Height: 8 cm

#### Perimeter:
\[
\text{Perimeter} = 10 + 10 + 10 = 30 \, \text{cm}
\]

#### Area:
The formula for the area of a triangle is:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
Here, the base is 10 cm, and the height is 8 cm.
\[
\text{Area} = \frac{1}{2} \times 10 \times 8 = \frac{1}{2} \times 80 = 40 \, \text{cm}^2
\]

#### Final Answers:
\[
\text{Perimeter} = 30 \, \text{cm}, \quad \text{Area} = 40 \, \text{cm}^2
\]

---

6. Purple Triangle

#### Dimensions:
- Sides: 9 m, 9 m, 9 m (equilateral triangle)
- Height: 8 m

#### Perimeter:
\[
\text{Perimeter} = 9 + 9 + 9 = 27 \, \text{m}
\]

#### Area:
The formula for the area of a triangle is:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
Here, the base is 9 m, and the height is 8 m.
\[
\text{Area} = \frac{1}{2} \times 9 \times 8 = \frac{1}{2} \times 72 = 36 \, \text{m}^2
\]

#### Final Answers:
\[
\text{Perimeter} = 27 \, \text{m}, \quad \text{Area} = 36 \, \text{m}^2
\]

---

Final Summary of Answers:

1. Orange Triangle:
\[
\text{Perimeter} = 14 \, \text{cm}, \quad \text{Area} = 12 \, \text{cm}^2
\]

2. Blue Triangle:
\[
\text{Perimeter} = 17 \, \text{cm}, \quad \text{Area} \approx 7.64 \, \text{cm}^2
\]

3. Green Triangle:
\[
\text{Perimeter} = 26 \, \text{cm}, \quad \text{Area} \approx 28.62 \, \text{cm}^2
\]

4. Pink Triangle:
\[
\text{Perimeter} = 36 \, \text{cm}, \quad \text{Area} \approx 61.48 \, \text{cm}^2
\]

5. Red Triangle:
\[
\text{Perimeter} = 30 \, \text{cm}, \quad \text{Area} = 40 \, \text{cm}^2
\]

6. Purple Triangle:
\[
\text{Perimeter} = 27 \, \text{m}, \quad \text{Area} = 36 \, \text{m}^2
\]

---

Boxed Final Answers:

\[
\boxed{
\begin{array}{ll}
\text{Orange Triangle:} & \text{Perimeter} = 14 \, \text{cm}, \, \text{Area} = 12 \, \text{cm}^2 \\
\text{Blue Triangle:} & \text{Perimeter} = 17 \, \text{cm}, \, \text{Area} \approx 7.64 \, \text{cm}^2 \\
\text{Green Triangle:} & \text{Perimeter} = 26 \, \text{cm}, \, \text{Area} \approx 28.62 \, \text{cm}^2 \\
\text{Pink Triangle:} & \text{Perimeter} = 36 \, \text{cm}, \, \text{Area} \approx 61.48 \, \text{cm}^2 \\
\text{Red Triangle:} & \text{Perimeter} = 30 \, \text{cm}, \, \text{Area} = 40 \, \text{cm}^2 \\
\text{Purple Triangle:} & \text{Perimeter} = 27 \, \text{m}, \, \text{Area} = 36 \, \text{m}^2 \\
\end{array}
}
\]