Areas in everyday situations · Grade 10 · 3 units
In Areas in everyday situations (Grade 10 · 3 units) you practise 6 skills: The area of a basic shape · The area of a circle · The area of a composite shape · A missing length from the area · 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 basic shape
For example: The lengths are in centimetres. What is the area of the rectangle?
Answer and solution
The answer: 96 cm²
The area: 24 × 4 = 96
The area of a circle
For example: The radius of the circle is 10 cm. What is the area of the circle? Give your answer in terms of π .
Answer and solution
The answer: 100π
The area of a circle is π times the radius squared. π × 10² = 100π The area of the circle is 100π cm².
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
A missing length from the area
For example: The area of a triangle is 119 cm², and its base is 14 cm. What is the height to the base?
Answer and solution
The answer: 17 cm
The height: 2 × 119 ÷ 14 = 17
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 shekels a square metre. How much will it cost to tile the whole floor?
Answer and solution
The answer: 2160 shekels
The area of the floor: 3 × 12 = 36 m². The cost: 36 times 60 shekels, that is 2,160 shekels.
Not on the site yet
Parts of this topic that are not built yet: Estimating an area · Making different shapes of the same area.
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 Israeli Ministry of Education’s high school maths curriculum at 3 units (grades 10 and 11).