Perimeter and area together · Year 10
In Perimeter and area together (Year 10) you practise 3 skills: 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
From the perimeter to the area and back
For example: The perimeter of a square is 80 cm. What is its area?
Answer and solution
The answer: 400 cm²
The side: 80 ÷ 4 = 20 . The area: 20² = 400
Graphs of perimeter and area
For example: The picture shows three graphs. One of them shows the perimeter of a square against its side, and one shows its area.
Which graph shows the perimeter?- A
- B
- C
Answer and solution
The answer: B
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
For example: A rectangle has a perimeter of 16 cm. Which length of the side x gives the greatest area?
- 2
- 7
- 4
Answer and solution
The answer: 4
The areas: 2 × 6 = 12 , 4 × 4 = 16 , 7 × 1 = 7 . The greatest is when the rectangle is a square, with side 4 cm.
The exercises are made by rules and the answers are worked out in code, so there are new exercises every time. The topic follows the national curriculum in England: mathematics (key stages 3 and 4).