Math worksheet for practicing area and perimeter calculations with diagrams and examples.

It looks like you've uploaded a worksheet titled "Area and Perimeter: Rectangles and Squares", which includes several problems involving finding the length, width, area, or perimeter of rectangles and squares. I'll go through each problem step by step and explain how to solve them.

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Problem 1:

> The area of a rectangular field is 180 square meters. The width is 12 meters. Find the length.

Given:
- Area = 180 m²
- Width = 12 m

Formula for area of a rectangle:
\[
\text{Area} = \text{Length} \times \text{Width}
\]

So,
\[
180 = \text{Length} \times 12
\]

Solve for Length:
\[
\text{Length} = \frac{180}{12} = 15 \text{ meters}
\]

✔ Answer: The length of the rectangular field is 15 meters.

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Problem 2:

> Find the perimeter of the field.

We now know:
- Length = 15 m
- Width = 12 m

Formula for perimeter of a rectangle:
\[
P = 2 \times (\text{Length} + \text{Width})
\]

\[
P = 2 \times (15 + 12) = 2 \times 27 = 54 \text{ meters}
\]

✔ Answer: The perimeter of the rectangular field is 54 meters.

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Problem 3:

> The area of a rectangular pool is 80 square meters. The length of the pool is 16 meters. Find the width.

Given:
- Area = 80 m²
- Length = 16 m

Use the area formula:
\[
\text{Area} = \text{Length} \times \text{Width}
\]
\[
80 = 16 \times \text{Width}
\]

Solve for Width:
\[
\text{Width} = \frac{80}{16} = 5 \text{ meters}
\]

✔ Answer: The width of the rectangular pool is 5 meters.

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Problem 4:

> Find the perimeter of the pool.

Now we have:
- Length = 16 m
- Width = 5 m

Use the perimeter formula:
\[
P = 2 \times (16 + 5) = 2 \times 21 = 42 \text{ meters}
\]

✔ Answer: The perimeter of the rectangular pool is 42 meters.

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Problem 5:

> Find the unknown side of each figure. Then find the perimeter of each figure.

This section has two figures:

#### Figure A:
- One side is 3 m
- Another side is 4 m
- It's a rectangle, so opposite sides are equal.

So, sides are: 3 m, 4 m, 3 m, 4 m

Perimeter:
\[
P = 2 \times (3 + 4) = 2 \times 7 = 14 \text{ m}
\]

✔ Perimeter = 14 meters

#### Figure B:
- Sides: 5 m, 3 m, 5 m, 3 m → also a rectangle

Perimeter:
\[
P = 2 \times (5 + 3) = 2 \times 8 = 16 \text{ m}
\]

✔ Perimeter = 16 meters

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1. Length of field | 15 meters |
| 2. Perimeter of field | 54 meters |
| 3. Width of pool | 5 meters |
| 4. Perimeter of pool | 42 meters |
| 5A. Perimeter | 14 meters |
| 5B. Perimeter | 16 meters |

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🔍 Explanation Recap:

- Area = Length × Width → used to find missing dimension.
- Perimeter = 2 × (Length + Width) → adds up all sides.
- Always double-check units (meters, square meters).
- For rectangles, opposite sides are equal.

Let me know if you'd like this turned into a printable solution sheet or need help with similar problems!