Key points
A rectilinear (shape)A shape made up of straight lines and right angles. shape may be a squareA regular quadrilateral. All four sides are equal in length and all four angles are right angles. or a rectangleA quadrilateral with opposite pairs of sides that are both equal in length and parallel. All four angles are right angles. or, as a compound shape (composite shape)A shape formed by combining two or more shapes. , it can look like two or more rectangles joined together.
For a shape drawn on a grid the areaA measure of the size of any plane surface or 2D shape. Area is measured in square units, for example, square centimetres or square metres: cm虏 or m虏. may be found by counting squares. Area is measured in square units, including cm虏 and m虏.
The calculation for finding the area of a square or a rectangle is found by using a formulaA fact, rule, or principle that is expressed in words or in mathematical symbols. Plural: formulae..
The total area of a compound shape is found by adding up the areas of the rectangles that have created the whole shape. This may be done in more than one way. The calculation may use a subtraction of areas where a rectangle has been removed from a larger rectangle.
Counting squares to find an area and working out the area of a square
To find the area of a rectilinear shape drawn on a grid:
- Count the squares inside the shape.
To calculate the area of a square:
- Multiply the length of one side by itself, this means the length is squared. For a whole number length, the value of the area is a square numberThe result of multiplying an integer by itself. It can be written as the product of two equal integers..
To calculate the side length of a square:
- Find the square rootA number whose square is equal to the given number, 鈭9 = 3, 3虏 = 9. The value may also be negative, eg (-3)虏 = 9 of the area of the square.
An integerIntegers are numbers with no fraction or decimal part. They can be positive, negative or zero. 42, 8, and 10000 are examples of integers. value for the length of one side of a square will result in an integer value for the area of a square, which is a square number. A square number is the result of multiplying an integer by itself and can be represented by a square on a grid.
Examples
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Question
Find the area of a square with side-length 1郯5 metres.
The area of a square is the side-length multiplied by itself. The side-length is squared.
1郯5虏 = 1郯5 脳 1郯5 = 2郯25
The area of the square is 2郯25 m虏.
How to work out the area of a rectangle
The area of a rectangle is measured in square units including cm虏 and m虏.
To work out the area of a rectangle:
- Check that the length and width of the rectangle are measured in the same units. If necessary, convert the units so that they match.
- Multiply the length by the width.
- Write the answer with the correct square units.
To work out the length or width of a rectangle:
- Divide the given area by the given width/length.
- Write the answer in the correct unit of length.
Examples
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Question
Find the area of the rectangle in square metres.
To calculate the area of the rectangle in square metres, both dimensions must be given in metres. The length of the rectangle is 9 m. The width of the rectangle is 250 cm. The width must be converted into metres.
250 cm is 2郯5 m.
The area of the rectangle is its length multiplied by its width, 9 脳 2郯5 = 22郯5
The area of the rectangle is 22郯5 m虏.
How to find the area of a compound shape
The area of a compound shape (composite shape)A shape formed by combining two or more shapes. may be calculated either by adding rectangles that create the shape or by subtracting a cut-out rectangle from a larger rectangle. Sometimes there is more than one way to work out the area of a compound shape.
To find the area of a compound shape using addition:
- Split the compound shape into rectangles that make the shape.
- For each separate rectangle, multiply the length and width to get its area.
- Add the separate rectangle areas to get the total area of the shape.
To find the area of a compound shape by using subtraction:
- Identify the large rectangle and the cut-out rectangle.
- For each rectangle, multiply the length and width to find its area.
- Subtract the cut-out rectangle area from the large rectangle area to find the area of the compound shape.
Example
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Practise finding the area of squares, rectangles and compound shapes
Quiz
Practise finding the area of squares, rectangles and compound shapes in this quiz. You may need a pen and paper to help you with your answers.
Real-life maths
An interior designer will calculate floor area when changing the floor covering in a room. Flooring materials, including laminate slats, are sold by the square metre.
For a rectangular floor measuring 4 m by 3 m the total area would be 4 脳 3 = 12 m虏. Laminate slats may come in packs that will cover 1郯8 m虏.
The number of packs needed is found by dividing the total area of the floor by the area coverage of each pack,12 梅 1郯8 = 6鈭6
The designer will need to buy seven packs so that they have sufficient laminate slats to cover the whole floor.
Game - Divided Islands
Play the Divided Islands game! gamePlay the Divided Islands game!
Using your maths skills, help to build bridges and bring light back to the islands in this free game from 麻豆官网首页入口 Bitesize.
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