# Perimeter and area together · Grade 10 · 3 units

> Perimeter and area together, Grade 10 · 3 units: The greatest area and more. Explanation, worked examples and free practice following the Israeli curriculum.

In Perimeter and area together (Grade 10 · 3 units) you practise 4 skills: Which is the perimeter and which the area · From the perimeter to the area and back · Graphs of perimeter and area · The greatest area.

The perimeter is the length of the line round a shape, measured in units of length such as metres. The area is how much space the shape covers, measured in units of area such as square metres.

Fences, frames and kerb stones depend on the perimeter. Paving, grass and glass depend on the area. A price per metre goes with the perimeter, and a price per square metre goes with the area.

For a square with side x, the perimeter is 4x and the area is x². The graph of the perimeter is a straight line from the origin, and the graph of the area curves and rises faster and faster.

Of all the rectangles with the same perimeter, the square has the greatest area. To find the greatest area you can make a table of the area for each length of side and pick the largest.

**Tip:** Before you answer, ask: is it the line round the shape, or what is inside?

## What you learn

### Which is the perimeter and which the area

- Example: Kerb stones are laid round a square yard, and the yard itself is paved. Does the amount of kerb stones needed depend on the perimeter or on the area?
- Options: The area · The perimeter
- Answer: The perimeter
- Solution: The amount of kerb stones is measured along the line round the shape, so it depends on the perimeter.

### From the perimeter to the area and back

- Example: The perimeter of a square is 80 cm. What is its area?
- Answer: 400 cm²
- Solution: The side: 80 ÷ 4 = 20 . The area: 20² = 400

### Graphs of perimeter and area

- Example: The picture shows three graphs. One of them shows the perimeter of a square against its side, and one shows its area. (Three graphs on the same axes, labelled A, B and C) Which graph shows the perimeter?
- Options: A · B · C
- Answer: B
- Solution: Graph B is a straight line from the origin that rises by 4 for each unit of side, so it is the perimeter.

### The greatest area

- Example: A rectangle has a perimeter of 16 cm. Which length of the side x gives the greatest area?
- Options: 2 · 7 · 4
- Answer: 4
- Solution: The areas: 2 × 6 = 12 , 4 × 4 = 16 , 7 × 1 = 7 . The greatest is when the rectangle is a square, with side 4 cm.

## Not on the site yet

- Sketching the area graph by hand
- Estimating

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).

[Practise on the site](https://kixplo.com/il/en/) · [All Grade 10 · 3 units topics](https://kixplo.com/il/en/math/grade-10-3u/)