# Areas in everyday situations · Year 10

> Areas in everyday situations, Year 10: Changing the dimensions and more. Explanation, worked examples and free practice for the national curriculum in England.

In Areas in everyday situations (Year 10) you practise 3 skills: The area of a composite shape · Changing the dimensions · Costs by area.

The area of a shape is how much space it covers, measured in square units: cm² or m². The area of a rectangle is its length times its width, a triangle’s is its base times the height to it divided by 2, and a parallelogram’s is a side times the height to it.

The area of a rhombus is the product of its diagonals divided by 2, and a trapezium’s is the sum of its parallel sides times the height divided by 2. The area of a circle is π times the radius squared, and π is about 3.14.

Split a composite shape into simple shapes and add their areas, or complete it to a simple shape and take away what was added.

When one side is multiplied by a number, the area is multiplied by the same number. When both sides are, the area is multiplied by that number squared. A square metre is 10,000 cm².

**Tip:** Write the square unit beside every answer, and check every length is in the same unit before you multiply.

## What you learn

### The area of a composite shape

- Example: The floor of a room is a rectangle with a rectangular corner missing. (A floor shaped as a rectangle with a corner missing, with the lengths of its sides) The lengths are in metres. What is the area of the floor?
- Answer: 60 m²
- Solution: The whole rectangle: 6 × 12 = 72 . The missing corner: 2 × 6 = 12 . The floor: 72 − 12 = 60

### Changing the dimensions

- Example: The lengths in the rectangle are in centimetres. (A rectangle with the lengths of two neighbouring sides) The side of length 5 is made 2 times as long. What is the area of the new rectangle?
- Answer: 150 cm²
- Solution: Before: 5 × 15 = 75 . After: 2 × 75 = 150

### Costs by area

- Example: The floor of a rectangular room. The lengths are in metres. (A rectangular floor with the lengths of two neighbouring sides) Tiling costs £60 a square metre. How much will it cost to tile the whole floor?
- Answer: £2160
- Solution: The area of the floor: 3 × 12 = 36 m². The cost: 36 times £60, that is £2,160.

The exercises are made by rules and the answers are worked out in code. The topic follows the national curriculum in England: mathematics (key stages 3 and 4).

[Practise on the site](https://kixplo.com/uk/en/) · [All Year 10 topics](https://kixplo.com/uk/en/maths/year-10/)