area and volume using formulae. finding area and perimeter of a square or rectangle area is the...
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Area and Volume
Using formulae
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Finding Area and Perimeter of a Square or Rectangle
• Area is the measure of the amount of space a shape covers
• Perimeter is the distance all the way around the outside.
length
width
Area of a rectangle = length x width
Perimeter = 2(length and width)
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Parallelogram
Length
Perpendicular height
Area of a parallelogram:
length x perpendicular height
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Trapezium
Perpendicular height
Length a
Length b
Area of a trapezium:
( length a + length b) x perpendicular height
(a+b) x h
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Shape Area PerimeterTriangle ½ (LxW) Add 3 sides
Square LxW 2(L+W)
Rectangle LxW 2(L+W)
Parallelogram L x Height 2(L+W)
Trapezium (A + B) x Height
2
Add all 4 sides
Circle r² x D
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To Find Area Complicated Shapes
1. Split them up into basic shapes
2. Work out the area of each bit separately
3. The add them altogether
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Perimeters of Complicated Shapes 1. Put a dot in one
corner then go around the shape
2. Write down the length of every side as you go
3. Even sides that have no length given you need to work out
4. Keep going until you get to the dot
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Areas and Volumes of 3D Shapes
Volume of a cuboid
• The volume of a 3D shape is a measure of the amount of space it occupies
• Typical units of measure are cubic centimetres (cm³) and cubic metres (m³)
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Volume of a Cuboid
• The volume of a cuboid can be written as
length x width x height
= l x w x h
Or you could think of it as the area of the cross section multiplied by the height
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Volume of a Prism
• A prism is a 3D shape with the same cross section all along its length
• To calculate the volume of the prism you need to find the area of the cross section and multiply it by the height or length
Volume of prism
= area of cross section x length
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Finding the Area of a Prism
This shape is a triangular
The volume is
Area of cross section x length