Algebraic Perimeters Worksheet | Printable PDF Worksheets - Free Printable

Let's solve the Algebraic Perimeters worksheet step by step. The goal is to find the perimeter of each shape as an algebraic expression.

---

🔷 Section A: Triangles

We add up all the side lengths.

1. Triangle with sides: a, 2a, 4a
$$
\text{Perimeter} = a + 2a + 4a = 7a
$$

2. Triangle with sides: 6b, 5b, b
$$
\text{Perimeter} = 6b + 5b + b = 12b
$$

3. Triangle with sides: 3w, 2w, 4w
$$
\text{Perimeter} = 3w + 2w + 4w = 9w
$$

4. Isosceles triangle (two equal sides marked with ticks): sides 8x, 8x, 2x
$$
\text{Perimeter} = 8x + 8x + 2x = 18x
$$

5. Isosceles triangle (two equal sides marked with ticks): sides s, 5s, s
$$
\text{Perimeter} = s + 5s + s = 7s
$$

✔ Section A Answers:
- 7a
- 12b
- 9w
- 18x
- 7s

---

🔷 Section B: Rectangles and Parallelograms

For rectangles and parallelograms, opposite sides are equal.

1. Rectangle: length = b, width = 3b
$$
\text{Perimeter} = 2(b + 3b) = 2(4b) = 8b
$$

2. Rectangle: length = 4t, width = t
$$
\text{Perimeter} = 2(4t + t) = 2(5t) = 10t
$$

3. Rectangle: length = 5g, width = g
$$
\text{Perimeter} = 2(5g + g) = 2(6g) = 12g
$$

4. Rectangle: length = 7h, width = 2h
$$
\text{Perimeter} = 2(7h + 2h) = 2(9h) = 18h
$$

5. Rectangle: length = 20e, width = 9e
$$
\text{Perimeter} = 2(20e + 9e) = 2(29e) = 58e
$$

6. Rectangle: length = 5x, width = y
$$
\text{Perimeter} = 2(5x + y) = 10x + 2y
$$

7. Rectangle: length = 6s, width = t
$$
\text{Perimeter} = 2(6s + t) = 12s + 2t
$$

8. Rectangle: length = 7u, width = z
$$
\text{Perimeter} = 2(7u + z) = 14u + 2z
$$

9. Rectangle: length = 3c, width = 2d
$$
\text{Perimeter} = 2(3c + 2d) = 6c + 4d
$$

✔ Section B Answers:
- 8b
- 10t
- 12g
- 18h
- 58e
- 10x + 2y
- 12s + 2t
- 14u + 2z
- 6c + 4d

---

🔷 Section C: Squares and Rhombuses

All sides are equal in squares and rhombuses (indicated by tick marks).

1. Square: side = f
$$
\text{Perimeter} = 4f
$$

2. Square: side = 3j
$$
\text{Perimeter} = 4 \times 3j = 12j
$$

3. Square: side = 5r
$$
\text{Perimeter} = 4 \times 5r = 20r
$$

4. Rhombus (diamond shape): side = a + b
$$
\text{Perimeter} = 4(a + b) = 4a + 4b
$$

5. Square: side = 2p + q
$$
\text{Perimeter} = 4(2p + q) = 8p + 4q
$$

✔ Section C Answers:
- 4f
- 12j
- 20r
- 4a + 4b
- 8p + 4q

---

🔷 Section D: Regular Polygons

All sides are equal (indicated by tick marks).

1. Regular Pentagon: side = y
$$
\text{Perimeter} = 5y
$$

2. Regular Hexagon: side = n + m
$$
\text{Perimeter} = 6(n + m) = 6n + 6m
$$

3. Rhombus (parallelogram with equal sides): side = k - l
$$
\text{Perimeter} = 4(k - l) = 4k - 4l
$$

✔ Section D Answers:
- 5y
- 6n + 6m
- 4k - 4l

---

✔ Final Summary of All Answers:

#### Section A (Triangles):
1. $ 7a $
2. $ 12b $
3. $ 9w $
4. $ 18x $
5. $ 7s $

#### Section B (Rectangles):
1. $ 8b $
2. $ 10t $
3. $ 12g $
4. $ 18h $
5. $ 58e $
6. $ 10x + 2y $
7. $ 12s + 2t $
8. $ 14u + 2z $
9. $ 6c + 4d $

#### Section C (Squares/Rhombuses):
1. $ 4f $
2. $ 12j $
3. $ 20r $
4. $ 4a + 4b $
5. $ 8p + 4q $

#### Section D (Polygons):
1. $ 5y $
2. $ 6n + 6m $
3. $ 4k - 4l $

---

📝 Explanation:

- Perimeter is the total distance around a shape.
- For polygons, sum all side lengths.
- Use algebraic simplification: combine like terms.
- In shapes with equal sides (marked with ticks), use multiplication: e.g., 4 × side for a square.
- For rectangles, use formula: $ P = 2(\text{length} + \text{width}) $

Let me know if you'd like this formatted as a printable answer sheet!