# Perimeters in everyday situations · Grade 10 · 3 units

> Perimeters in everyday situations, Grade 10 · 3 units: Costs by perimeter and more. Explanation, worked examples and free practice following the Israeli curriculum.

In Perimeters in everyday situations (Grade 10 · 3 units) you practise 5 skills: The perimeter of a polygon · The circumference of a circle · A missing length from the perimeter · Changing the dimensions · Costs by perimeter.

The perimeter of a shape is the sum of the lengths of all its sides, the length of the line that goes round it. When sides are equal you can multiply instead of adding: a square’s perimeter is four times its side, and a rectangle’s is twice the sum of two neighbouring sides.

The circumference of a circle is π times the diameter. As an approximation, π is about 3.14.

When you know the perimeter and most of the sides, you can find a missing side: take away the known sides and divide by how many sides are missing. Before you work it out, check that every length is in the same unit.

When every side is multiplied by a number, the perimeter is multiplied by the same number. The cost of a fence is the perimeter times the price of one metre.

**Tip:** Sketch the shape and write the length of every side, even the ones not given: that way no side is forgotten.

## What you learn

### The perimeter of a polygon

- Example: (A rectangle with the lengths of two neighbouring sides) The lengths are in centimetres. What is the perimeter of the shape?
- Answer: 68 cm
- Solution: Add all the sides: 29 + 5 + 29 + 5 = 68

### The circumference of a circle

- Example: (A circle with a radius of length 10) The radius of the circle is 10 cm. What is the circumference of the circle? Give your answer in terms of π .
- Answer: 20π
- Solution: The diameter: 2 × 10 = 20 The circumference of a circle is π times the diameter. π × 20 = 20π

### A missing length from the perimeter

- Example: (A rectangle with the length of one side and a question mark on the next side) The perimeter of the rectangle is 70 cm. How long is the side marked with a question mark?
- Answer: 6 cm
- Solution: The two known sides: 2 × 29 = 58 . The two missing sides: 70 − 58 = 12 , so each is 12 ÷ 2 = 6

### 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 7 is made 5 cm longer. What is the perimeter of the new rectangle?
- Answer: 72 cm
- Solution: The new side: 7 + 5 = 12 . The new perimeter: 2 × (12 + 24) = 72

### Costs by perimeter

- Example: A rectangular plot is to be fenced. The lengths are in metres. (A rectangular plot with the lengths of two neighbouring sides) One metre of fence costs 30 shekels. How much will it cost to fence the whole plot?
- Answer: 2460 shekels
- Solution: The perimeter: 2 × (12 + 29) = 82 metres. The cost: 82 times 30 shekels, that is 2,460 shekels.

## Not on the site yet

- Estimating a perimeter
- Measuring on site

The exercises are made by rules and the answers are worked out in code. The topic follows the Israeli Ministry of Education’s high school maths curriculum at 3 units (grades 10 and 11).

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