Areas in everyday situations · Year 10
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
For example: The floor of a room is a rectangle with a rectangular corner missing. The lengths are in metres. What is the area of the floor?
Answer and solution
The answer: 60 m²
The whole rectangle: 6 × 12 = 72 . The missing corner: 2 × 6 = 12 . The floor: 72 − 12 = 60
Changing the dimensions
For example: The lengths in the rectangle are in centimetres. The side of length 5 is made 2 times as long. What is the area of the new rectangle?
Answer and solution
The answer: 150 cm²
Before: 5 × 15 = 75 . After: 2 × 75 = 150
Costs by area
For example: The floor of a rectangular room. The lengths are in metres. Tiling costs £60 a square metre. How much will it cost to tile the whole floor?
Answer and solution
The answer: £2160
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, so there are new exercises every time. The topic follows the national curriculum in England: mathematics (key stages 3 and 4).