Worksheet titled "Area Word Problems" featuring five math problems that involve calculating areas in different contexts, including tables, a football pitch, a bedroom, a window, and a car park.

Let's solve each of these area word problems step by step, with clear explanations.

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1. Each table in a classroom is 110 cm long and 55 cm wide. What is the area of each table in square centimetres and square metres?

#### Step 1: Area in square centimetres
- Length = 110 cm
- Width = 55 cm
- Area = length × width
$$
110 \times 55 = 6050 \text{ cm}^2
$$

#### Step 2: Convert to square metres
We know:
- 1 m = 100 cm → 1 m² = 10,000 cm²
So:
$$
6050 \div 10000 = 0.605 \text{ m}^2
$$

✔ Answer:
- Area = 6050 cm² or 0.605 m²

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#### a) There are 16 tables in a classroom. What is the total area of the tables in the classroom in square metres?

- Area of one table = 0.605 m²
- Total area = $ 16 \times 0.605 = 9.68 \text{ m}^2 $

✔ Answer: 9.68 m²

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2. An artificial football pitch is 92 metres long and 41 metres wide. There is a border of grass all around the edge of the pitch that is 2 metres wide. What is the area of the whole artificial surface?

The artificial surface includes the pitch plus the 2m grass border all around.

So we need to add 2m on each side (left/right and top/bottom).

- New length = $ 92 + 2 + 2 = 96 $ m
- New width = $ 41 + 2 + 2 = 45 $ m
- Total area = $ 96 \times 45 = 4320 \text{ m}^2 $

✔ Answer: 4320 m²

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#### a) If the cost of the pitch is £38 per square metre, what is the cost of installing the pitch?

- Cost = area × price per m²
$$
4320 \times 38 = £164,160
$$

✔ Answer: £164,160

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3. A bedroom is 3.5m long and 2.4m wide and 2.1m high. Ignoring the door and window, what is the total area of the walls in the bedroom?

We need the area of the four walls.

There are two pairs of opposite walls:

- Two walls: $ 3.5 \text{ m (length)} \times 2.1 \text{ m (height)} $
- Two walls: $ 2.4 \text{ m (width)} \times 2.1 \text{ m (height)} $

Calculate:
- First pair: $ 2 \times (3.5 \times 2.1) = 2 \times 7.35 = 14.7 \text{ m}^2 $
- Second pair: $ 2 \times (2.4 \times 2.1) = 2 \times 5.04 = 10.08 \text{ m}^2 $

Total wall area:
$$
14.7 + 10.08 = 24.78 \text{ m}^2
$$

✔ Answer: 24.78 m²

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#### a) A tin of paint will cover 20m². How many tins are needed if the walls all need 2 coats of paint?

- Total area to be painted = $ 24.78 \times 2 = 49.56 \text{ m}^2 $
- One tin covers 20 m²
- Number of tins = $ 49.56 \div 20 = 2.478 $

Since you can’t buy part of a tin, round up to next whole number → 3 tins

✔ Answer: 3 tins

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4. A window is 1.7m wide and 85cm high. What is the area of the window?

First, convert height to metres:
- 85 cm = 0.85 m

Area = $ 1.7 \times 0.85 = 1.445 \text{ m}^2 $

✔ Answer: 1.445 m²

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#### a) Three times the area of the window is needed for curtain material. What area of material is needed?

- $ 3 \times 1.445 = 4.335 \text{ m}^2 $

✔ Answer: 4.335 m²

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5. A car park space needs 8 square metres for 1 car. Just considering the spaces for parking, what dimensions for a car park would be needed for 62 cars?

- Total area needed = $ 62 \times 8 = 496 \text{ m}^2 $

Now, possible dimensions depend on layout. We just need any rectangle with area 496 m².

For example:
- $ 16 \text{ m} \times 31 \text{ m} = 496 \text{ m}^2 $
- Or $ 8 \text{ m} \times 62 \text{ m} $
- Or $ 32 \text{ m} \times 15.5 \text{ m} $

Any reasonable rectangular shape with area 496 m² works.

✔ Answer: Example: 32 m × 15.5 m (or any other combination)

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#### a) What else needs to be taken into account?

Besides the space for cars, consider:
- Access roads / driveways for cars to enter/exit
- Turning space for vehicles
- Pedestrian walkways
- Parking angles (angled vs parallel)
- Safety zones or buffer areas
- Lighting and signage
- Drainage and landscaping

✔ Answer: Access lanes, turning space, pedestrian paths, safety margins, lighting, and access routes.

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✔ Final Answers Summary:

1. Table area: 6050 cm², 0.605 m²
a) Total area of 16 tables: 9.68 m²

2. Artificial surface area: 4320 m²
a) Cost: £164,160

3. Wall area: 24.78 m²
a) Paint tins needed: 3 tins

4. Window area: 1.445 m²
a) Curtain material: 4.335 m²

5. Car park area: 496 m² (e.g., 32 m × 15.5 m)
a) Also consider: access roads, turning space, pedestrian paths, etc.

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