Math worksheet for calculating the area of rectangles using algebraic expressions.

Let's solve each problem step by step. The goal is to find the value of $ x $ using the given dimensions of the rectangle, and then compute the area using the formula:

$$
\text{Area} = \text{length} \times \text{width}
$$

We'll use the fact that opposite sides of a rectangle are equal, so if one side is labeled with an expression and another side has a known length, we can set up an equation to solve for $ x $. Then plug in $ x $ to find the area.

---

Problem 1

- One side: $ (2x + 10) $ cm
- Opposite side: 44 cm → So:
$$
2x + 10 = 44 \\
2x = 34 \\
x = 17
$$

Now find the area:
- Length = 44 cm
- Width = 8 cm (given)
- Area = $ 44 \times 8 = 352 $ cm²

✔ Answer:
$ x = 17 $, Area = $ 352 $ cm²

---

Problem 2

- One side: $ (2x - 4) $ in
- Opposite side: 32 in → So:
$$
2x - 4 = 32 \\
2x = 36 \\
x = 18
$$

Now find area:
- Length = 64 in
- Width = 32 in
- Area = $ 64 \times 32 = 2048 $ in²

✔ Answer:
$ x = 18 $, Area = $ 2048 $ in²

---

Problem 3

- One side: $ (x + 16) $ m
- Opposite side: 32 m → So:
$$
x + 16 = 32 \\
x = 16
$$

Now find area:
- Length = 32 m
- Width = 12 m
- Area = $ 32 \times 12 = 384 $ m²

✔ Answer:
$ x = 16 $, Area = $ 384 $ m²

---

Problem 4

- One side: $ (4x - 6) $ km
- Opposite side: 26 km → So:
$$
4x - 6 = 26 \\
4x = 32 \\
x = 8
$$

Now find area:
- Length = 26 km
- Width = 14 km
- Area = $ 26 \times 14 = 364 $ km²

✔ Answer:
$ x = 8 $, Area = $ 364 $ km²

---

Problem 5

- One side: $ (5x - 15) $ m
- Opposite side: 225 m → So:
$$
5x - 15 = 225 \\
5x = 240 \\
x = 48
$$

Now find area:
- Length = 225 m
- Width = 22 m
- Area = $ 225 \times 22 = 4950 $ m²

✔ Answer:
$ x = 48 $, Area = $ 4950 $ m²

---

Problem 6

- One side: $ (x + 2) $ cm
- Opposite side: 64 cm → So:
$$
x + 2 = 64 \\
x = 62
$$

Now find area:
- Length = 64 cm
- Width = 12 cm
- Area = $ 64 \times 12 = 768 $ cm²

✔ Answer:
$ x = 62 $, Area = $ 768 $ cm²

---

Problem 7

- One side: $ (8x - 54) $ ft
- Opposite side: 18 ft → So:
$$
8x - 54 = 18 \\
8x = 72 \\
x = 9
$$

Now find area:
- Length = 18 ft
- Width = 10 ft
- Area = $ 18 \times 10 = 180 $ ft²

✔ Answer:
$ x = 9 $, Area = $ 180 $ ft²

---

Problem 8

- One side: $ (x + 10) $ ft
- Opposite side: 60 ft → So:
$$
x + 10 = 60 \\
x = 50
$$

Now find area:
- Length = 60 ft
- Width = 16 ft
- Area = $ 60 \times 16 = 960 $ ft²

✔ Answer:
$ x = 50 $, Area = $ 960 $ ft²

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✔ Final Answers Summary:

| Problem | $ x $ | Area |
|--------|--------|------|
| 1 | 17 | 352 cm² |
| 2 | 18 | 2048 in² |
| 3 | 16 | 384 m² |
| 4 | 8 | 364 km² |
| 5 | 48 | 4950 m² |
| 6 | 62 | 768 cm² |
| 7 | 9 | 180 ft² |
| 8 | 50 | 960 ft² |

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